base64 is meant for encoding high-bit data into a form suitable for
transmission under the 7bit rules. It has nothing to do with
compression.
If you want to compress a 64-byte string of 0's and 1's, use
pack .
# The sender packs it
my $p = pack 'b4' , $str ;
# And the receiver unpacks it like this:
print unpack 'b4', $p;