The generator matrix

 1  0  0  0  1  1  1  0  1  1  1  1  2  2  1  1  1  1  1  1
 0  1  0  0  0  1  1  1  0  2  3  3  1  1  0  3  2  1  0  0
 0  0  1  0  1  1  0  1  0  1  1  0  0  1  3  2  3  3  2  0
 0  0  0  1  1  0  1  1  1  0  1  0  1  0  3  1  2  1  3  0
 0  0  0  0  2  0  0  0  0  0  0  2  0  2  2  0  2  2  0  2
 0  0  0  0  0  2  0  0  0  0  2  0  0  2  2  2  0  2  0  0
 0  0  0  0  0  0  2  0  0  2  2  2  2  0  0  2  0  0  2  2
 0  0  0  0  0  0  0  2  0  2  0  0  2  0  2  0  2  2  2  0
 0  0  0  0  0  0  0  0  2  2  2  2  2  2  0  0  2  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+48x^12+102x^13+214x^14+308x^15+445x^16+644x^17+804x^18+996x^19+1060x^20+976x^21+829x^22+668x^23+442x^24+316x^25+196x^26+76x^27+52x^28+10x^29+4x^30+1x^38

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 seconds.