Ask for what you want matched. In this case, you most likely want everything up to the next double-quote, yes? If so, something like this should work:

  my ( $code ) = ( $line =~ /code="([^"]+)"/ );
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The use (and abuse) of regexes to match HTML content has been beaten to death. If you want stronger results, consider using a module designed to parse HTML. This is also covered in the fantastic book Mastering Regular Expressions.

Some cases to watch out for:

  <!-- watch out for greedy matching -->
  <tag code="blah" attr="nothing">

  <!-- and for less-than characters in attribute values
       (which is likely illegal, but HTML in the wild
       is notoriously nasty this way) -->
  <tag code="<bang!>">

  <!-- finally, make sure you can handle multiple-line tags -->
  <tag foo="bar"
       code="nothing">
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