The generator matrix

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

generates a code of length 20 over Z4 who´s minimum homogenous weight is 13.

Homogenous weight enumerator: w(x)=1x^0+22x^13+67x^14+104x^15+141x^16+166x^17+189x^18+204x^19+230x^20+246x^21+209x^22+176x^23+102x^24+74x^25+75x^26+28x^27+6x^28+4x^29+4x^30

The gray image is a code over GF(2) with n=40, k=11 and d=13.
This code was found by Heurico 1.10 in 0.047 seconds.