Simply open Windows Explorer and click into the search box. You should see the "Search Tools" appear in the top bar. Click on "Advanced options" and you will see some selections for "In non-indexed locations", make sure that "File Contents" is selected. Note that this will slow down your searches - probably rather a lot! But this ensures that the contents will be searched even if your file is hidden away in a location that Windows Search does not index.
You could also make sure that Windows Search Index is indexing all possible locations.
Be warned though that I've never found Windows Search all that reliable.
UPDATE: If you are not finding Windows Search all that reliable, you could try a GREP tool for Windows. Please note that I've not tried any of these (I use SharePoint for document management).
- dnGrep seems the most likely candidate. It has a plugin to read Word 2007+ files
- Funduc have a free macro for Word that might do what you want. They also have more powerful but non-free tools.
- The free Windows GREP tool will search in binary files but I don't know whether it will pick up text in docx files.
- The shareware PowerGREP will search in both .doc and .docx files but it is incredibly expensive! EUR119 for a single license! There is a free trial though.
- Common Resource Grep is free but is Linux only.