I worked out a solution, but the problem is that it prepends to $out instead of appending, so converting $out to a file handle is out.

$in    = '67567';
$carry = 126;

$out = sprintf('%06d', substr($in, -3, 3, '') * 222 + $carry);

while (length($in)) {
   substr($out, 0, 3, sprintf('%04d',
      substr($out, 0, 3) + substr($in, -1, 1, '') * 222
   ));
}

$out =~ s/^0+//;

print($out, "\n");
[download]

You'll need to put some work into reversing it. Show some effort.