The generator matrix

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

generates a code of length 22 over Z4 who´s minimum homogenous weight is 12.

Homogenous weight enumerator: w(x)=1x^0+47x^12+170x^13+320x^14+498x^15+852x^16+1324x^17+1818x^18+2616x^19+3219x^20+3564x^21+3880x^22+3628x^23+3164x^24+2576x^25+1900x^26+1336x^27+845x^28+538x^29+264x^30+114x^31+63x^32+20x^33+10x^34+1x^36

The gray image is a code over GF(2) with n=44, k=15 and d=12.
This code was found by Heurico 1.10 in 5.85 seconds.