The generator matrix

1 0 0 0 0 0 1 1 1 1 0 0 2 1 2 1 2 0 1 1 1 1
0 1 0 0 0 0 0 0 0 0 0 1 1 1 2 2 1 2 1 3 1 0
0 0 1 0 0 0 0 1 1 2 1 2 1 2 0 1 0 1 2 1 2 0
0 0 0 1 0 0 0 1 2 3 3 1 0 2 1 0 2 0 0 3 3 0
0 0 0 0 1 0 1 0 1 3 1 2 3 1 1 0 3 2 0 2 3 0
0 0 0 0 0 1 1 3 2 0 3 3 1 2 0 3 1 0 1 2 3 0
0 0 0 0 0 0 2 2 0 2 2 2 2 2 2 2 0 2 0 0 0 2

generates a code of length 22 over Z4 who´s minimum homogenous weight is 14.

Homogenous weight enumerator: w(x)=1x^0+71x^14+126x^15+237x^16+314x^17+494x^18+636x^19+779x^20+926x^21+907x^22+1028x^23+825x^24+662x^25+505x^26+300x^27+193x^28+82x^29+66x^30+22x^31+13x^32+5x^34

The gray image is a code over GF(2) with n=44, k=13 and d=14.
This code was found by Heurico 1.10 in 0.64 seconds.