sending an email form is not working (Button doesn't do anything)

Question

I've been trying for the longest time to get the email form to work and be able to send an email copy to my personal email from my website. When I hit the submit button, the console communicates with the PHP code but nothing happens. I tried to change the line <form class="form-contact contact_form" action="mailto:my@email.com" method="post" id="contactForm" novalidate="novalidate">

to

<form class="form-contact contact_form" action="code.php">

but that just invoked the code.php page and still does nothing. I really want to fix this by myself so I would appreciate if you can give me a hint on how to fix it.

HTML code

<!-- Form begins -->
          <form class="form-contact contact_form" action="code.php" method="post" id="contactForm" novalidate="novalidate">
            <div class="row">
              <div class="col-12">
                <div class="form-group">

                    <textarea class="form-control w-100" name="message" id="message" cols="30" rows="9" onfocus="this.placeholder = ''" onblur="this.placeholder = 'Enter Message'" placeholder = 'Enter Message'></textarea>
                </div>
              </div>
              <div class="col-sm-6">
                <div class="form-group">
                  <input class="form-control" name="name" id="name" type="text" onfocus="this.placeholder = ''" onblur="this.placeholder = 'Enter your name'" placeholder = 'Enter your name'>
                </div>
              </div>
              <div class="col-sm-6">
                <div class="form-group">
                  <input class="form-control" name="email" id="email" type="email" onfocus="this.placeholder = ''" onblur="this.placeholder = 'Enter email address'" placeholder = 'Enter email address'>
                </div>
              </div>
              <div class="col-12">
                <div class="form-group">
                  <input class="form-control" name="subject" id="subject" type="text" onfocus="this.placeholder = ''" onblur="this.placeholder = 'Enter Subject'" placeholder = 'Enter Subject'>
                </div>
              </div>
            </div>
            <div class="form-group mt-3">
              <button type="submit" class="button button-contactForm btn_4 boxed-btn">Send Message</button>
            </div>
          </form>
          <!-- Form Ends -->

JS Code

    // -------   Mail Send ajax

     $(document).ready(function() {
        var form = $('#contactForm'); // contact form
        var submit = $('.submit-btn'); // submit button
        var alert = $('.alert-msg'); // alert div for show alert message

        // form submit event
        form.on('submit', function(e) {
            e.preventDefault(); // prevent default form submit

            $.ajax({
                url: 'code.php', // form action url
                type: 'POST', // form submit method get/post
                dataType: 'html', // request type html/json/xml
                data: form.serialize(), // serialize form data
                beforeSend: function() {
                    alert.fadeOut();
                    submit.html('Sending....'); // change submit button text
                },
                success: function(data) {
                    alert.html(data).fadeIn(); // fade in response data
                    form.trigger('reset'); // reset form
                    submit.attr("style", "display: none !important");; // reset submit button text
                },
                error: function(e) {
                    console.log(e)
                }
            });
        });
    });

code.php file

<?php

    $to = "my@email.com";
    $from = $_REQUEST['email'];
    $name = $_REQUEST['name'];
    $subject = $_REQUEST['subject'];
    $number = $_REQUEST['number'];
    $cmessage = $_REQUEST['message'];

    $headers = "From: $from";
    $headers = "From: " . $from . "\r\n";
    $headers .= "Reply-To: ". $from . "\r\n";
    $headers .= "MIME-Version: 1.0\r\n";
    $headers .= "Content-Type: text/html; charset=ISO-8859-1\r\n";

    $subject = "You have a message from your Bitmap Photography.";

    $logo = 'img/logo.png';
    $link = '#';

    $body = "<!DOCTYPE html><html lang='en'><head><meta charset='UTF-8'><title>Express Mail</title></head><body>";
    $body .= "<table style='width: 100%;'>";
    $body .= "<thead style='text-align: center;'><tr><td style='border:none;' colspan='2'>";
    $body .= "<a href='{$link}'><img src='{$logo}' alt=''></a><br><br>";
    $body .= "</td></tr></thead><tbody><tr>";
    $body .= "<td style='border:none;'><strong>Name:</strong> {$name}</td>";
    $body .= "<td style='border:none;'><strong>Email:</strong> {$from}</td>";
    $body .= "</tr>";
    $body .= "<tr><td style='border:none;'><strong>Subject:</strong> {$csubject}</td></tr>";
    $body .= "<tr><td></td></tr>";
    $body .= "<tr><td colspan='2' style='border:none;'>{$cmessage}</td></tr>";
    $body .= "</tbody></table>";
    $body .= "</body></html>";

    $send = mail($to, $subject, $body, $headers);

?>