The generator matrix

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

generates a code of length 22 over Z4 who´s minimum homogenous weight is 11.

Homogenous weight enumerator: w(x)=1x^0+42x^11+159x^12+338x^13+627x^14+1024x^15+1591x^16+2638x^17+3843x^18+4980x^19+6293x^20+7192x^21+7466x^22+7324x^23+6466x^24+5232x^25+4066x^26+2782x^27+1665x^28+966x^29+499x^30+228x^31+78x^32+18x^33+11x^34+4x^35+3x^36

The gray image is a code over GF(2) with n=44, k=16 and d=11.
This code was found by Heurico 1.10 in 23.6 seconds.