The generator matrix

 1  0  0  0  0  0  1  1  1  2  1  2  2  1  1  1  1  0  1  2
 0  1  0  0  0  0  0  0  0  1  1  1  1  1  2  1  0  2  1  0
 0  0  1  0  0  0  0  0  3  0  1  2  1  3  2  0  2  1  0  1
 0  0  0  1  0  0  0  1  1  1  2  0  3  0  1  0  2  1  1  1
 0  0  0  0  1  0  1  1  0  1  2  3  0  2  2  1  0  0  2  2
 0  0  0  0  0  1  1  0  1  3  0  0  3  1  2  1  3  2  2  0
 0  0  0  0  0  0  2  0  2  2  2  0  0  0  2  2  0  2  2  2
 0  0  0  0  0  0  0  2  2  0  2  2  0  0  0  2  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+131x^12+194x^13+410x^14+590x^15+941x^16+1198x^17+1612x^18+2074x^19+1986x^20+2130x^21+1648x^22+1286x^23+930x^24+554x^25+404x^26+142x^27+107x^28+20x^29+22x^30+4x^31

The gray image is a code over GF(2) with n=40, k=14 and d=12.
This code was found by Heurico 1.16 in 8.07 seconds.