This one i tried in SQL2008, which can search from all the db at one go.
Create table #temp1 
(ServerName varchar(64), dbname varchar(64)
,spName varchar(128),ObjectType varchar(32), SearchString varchar(64))
Declare @dbid smallint, @dbname varchar(64), @longstr varchar(5000)
Declare @searhString VARCHAR(250)
set  @searhString='firstweek'
declare db_cursor cursor for 
select dbid, [name] 
from master..sysdatabases
where [name] not in ('master', 'model', 'msdb', 'tempdb', 'northwind', 'pubs')
open db_cursor
fetch next from db_cursor into @dbid, @dbname
while (@@fetch_status = 0)
begin
    PRINT 'DB='+@dbname
    set @longstr = 'Use ' + @dbname + char(13) +        
        'insert into #temp1 ' + char(13) +  
        'SELECT @@ServerName,  ''' + @dbname + ''', Name 
        , case  when [Type]= ''P'' Then ''Procedure''
                when[Type]= ''V'' Then ''View''
                when [Type]=  ''TF'' Then ''Table-Valued Function'' 
                when [Type]=  ''FN'' Then ''Function'' 
                when [Type]=  ''TR'' Then ''Trigger'' 
                else [Type]/*''Others''*/
                end 
        , '''+ @searhString +''' FROM  [SYS].[SYSCOMMEnTS]
        JOIN  [SYS].objects ON ID = object_id
        WHERE TEXT LIKE ''%' + @searhString + '%'''
 exec (@longstr)
 fetch next from db_cursor into @dbid, @dbname
end
close db_cursor
deallocate db_cursor
select * from #temp1
Drop table #temp1