If you want to match that exactly line and nothing else and extract no date, don't use a regex. Use eq:

use constant THE_LINE => q[      Code (inc. data)   RO Data    RW Data
+    ZI Data      Debug   Object Name];
...

if( $MapFile->[ $iterator ] eq THE_LINE ) {
    ...
}
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As for why your regex doesn't match.

Did you chomp the newlines off when you read the lines in? Does the leading whitespace contain tabs perhaps? Or elsewhere in the line?