The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+50x^13+114x^14+182x^15+252x^16+320x^17+409x^18+454x^19+497x^20+484x^21+413x^22+354x^23+261x^24+160x^25+83x^26+34x^27+11x^28+10x^29+5x^30+2x^32

The gray image is a code over GF(2) with n=40, k=12 and d=13.
This code was found by Heurico 1.16 in 0.328 seconds.