The generator matrix

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

generates a code of length 21 over Z4 who´s minimum homogenous weight is 11.

Homogenous weight enumerator: w(x)=1x^0+18x^11+75x^12+166x^13+241x^14+406x^15+658x^16+970x^17+1279x^18+1434x^19+1788x^20+2070x^21+1852x^22+1586x^23+1350x^24+1022x^25+680x^26+380x^27+217x^28+124x^29+43x^30+16x^31+7x^32+1x^34

The gray image is a code over GF(2) with n=42, k=14 and d=11.
This code was found by Heurico 1.10 in 1.56 seconds.