The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+54x^12+92x^13+216x^14+310x^15+472x^16+590x^17+824x^18+1022x^19+964x^20+1086x^21+816x^22+642x^23+500x^24+266x^25+184x^26+74x^27+54x^28+14x^29+8x^30+3x^32

The gray image is a code over GF(2) with n=40, k=13 and d=12.
This code was found by Heurico 1.16 in 1.09 seconds.