The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+38x^13+137x^14+204x^15+226x^16+314x^17+362x^18+454x^19+553x^20+466x^21+439x^22+386x^23+225x^24+134x^25+81x^26+42x^27+19x^28+8x^29+4x^30+2x^31+1x^34

The gray image is a code over GF(2) with n=40, k=12 and d=13.
This code was found by Heurico 1.10 in 0.125 seconds.