The generator matrix

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

generates a code of length 20 over Z4 who´s minimum homogenous weight is 12.

Homogenous weight enumerator: w(x)=1x^0+86x^12+92x^13+277x^14+310x^15+491x^16+600x^17+734x^18+996x^19+886x^20+1096x^21+792x^22+664x^23+500x^24+248x^25+226x^26+76x^27+84x^28+12x^29+19x^30+2x^31

The gray image is a code over GF(2) with n=40, k=13 and d=12.
This code was found by Heurico 1.10 in 0.465 seconds.