The generator matrix

 1  0  0  0  0  0  1  1  1  0  1  1  1  1  0  2  1  0  1  0  1  1
 0  1  0  0  0  0  0  0  0  1  2  3  3  1  1  2  1  0  3  2  2  0
 0  0  1  0  0  0  0  0  0  1  3  3  2  3  0  1  2  1  1  2  0  0
 0  0  0  1  0  0  0  1  1  1  0  2  2  1  3  2  3  0  3  1  2  0
 0  0  0  0  1  0  1  1  0  1  1  3  1  2  0  3  3  0  1  2  0  0
 0  0  0  0  0  1  1  0  1  1  0  3  0  3  1  3  1  3  2  1  1  0
 0  0  0  0  0  0  2  0  0  0  0  0  0  2  2  2  2  0  2  2  0  0
 0  0  0  0  0  0  0  2  0  2  2  0  0  2  2  2  2  2  0  2  0  0
 0  0  0  0  0  0  0  0  2  2  2  0  2  0  2  0  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+56x^12+140x^13+322x^14+506x^15+883x^16+1258x^17+1948x^18+2568x^19+3180x^20+3696x^21+3605x^22+3724x^23+3166x^24+2620x^25+1988x^26+1256x^27+852x^28+468x^29+320x^30+138x^31+54x^32+10x^33+8x^34+1x^38

The gray image is a code over GF(2) with n=44, k=15 and d=12.
This code was found by Heurico 1.16 in 14.2 seconds.