The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+75x^12+96x^13+306x^14+290x^15+486x^16+622x^17+688x^18+1010x^19+926x^20+1070x^21+796x^22+662x^23+480x^24+250x^25+240x^26+86x^27+79x^28+10x^29+18x^30+1x^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 1.22 seconds.