My first thought was m/(....).*\1/ but that would not detect overlapping repetitions. But I am sure such a regex exists.

I was looking to combine lookaheads with captures to check for dups, but then settled for using index to check for existance, and again, with the offset+1 from the first to check for duplicates.

My brute forcer finds 208 complient patterns in about a minute:

The second set of numbers is the order of the 4-bit patterns within the 19-bit solutions -- in the vague hope they might give some hint as to a generic algorithm -- now rendered unnecessary as Corion's discovered it is a solved problem.