The generator matrix

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

generates a code of length 21 over Z4 who´s minimum homogenous weight is 12.

Homogenous weight enumerator: w(x)=1x^0+128x^12+176x^13+506x^14+710x^15+1290x^16+1712x^17+2511x^18+3440x^19+3768x^20+4288x^21+3713x^22+3420x^23+2544x^24+1840x^25+1326x^26+608x^27+456x^28+176x^29+132x^30+14x^31+5x^32+3x^34+1x^38

The gray image is a code over GF(2) with n=42, k=15 and d=12.
This code was found by Heurico 1.16 in 20.6 seconds.