The generator matrix

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

generates a code of length 20 over Z4 who´s minimum homogenous weight is 11.

Homogenous weight enumerator: w(x)=1x^0+28x^11+63x^12+138x^13+232x^14+296x^15+428x^16+632x^17+837x^18+936x^19+944x^20+932x^21+836x^22+680x^23+506x^24+328x^25+202x^26+108x^27+41x^28+18x^29+4x^30+1x^32+1x^34

The gray image is a code over GF(2) with n=40, k=13 and d=11.
This code was found by Heurico 1.10 in 0.396 seconds.