The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+29x^14+74x^15+121x^16+228x^17+265x^18+284x^19+351x^20+428x^21+481x^22+420x^23+437x^24+368x^25+209x^26+172x^27+109x^28+60x^29+38x^30+10x^31+5x^32+4x^33+2x^34

The gray image is a code over GF(2) with n=44, k=12 and d=14.
This code was found by Heurico 1.10 in 0.141 seconds.