11101110 01101001 to
11011100 11010010
11011100 11010011
10111001 10100110
10111001 10100111
... x 8 bit variations. 

Convert them to bytes and then use one of the string efficient algos.  Matches on the needle will allow you to either know 100% (if its on the non shifted bytes) or at least that there is a possible match on the shifted bytes which can be verified at the bit level for the full match.