The generator matrix

 1  0  0  0  1  1  1  0  1  1  1  1  1  2  2  0  1  1  1  1
 0  1  0  0  0  1  1  1  2  2  3  3  3  1  1  1  0  0  2  0
 0  0  1  0  1  1  0  1  0  1  1  0  3  2  3  1  3  0  0  0
 0  0  0  1  1  0  1  1  1  0  1  0  2  3  0  1  2  3  1  0
 0  0  0  0  2  0  0  0  0  2  0  2  2  2  2  0  0  0  0  0
 0  0  0  0  0  2  0  0  2  2  2  2  0  2  2  2  0  2  0  0
 0  0  0  0  0  0  2  0  2  0  0  2  2  2  0  2  0  2  0  0
 0  0  0  0  0  0  0  2  2  0  2  2  2  2  2  0  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+37x^12+30x^13+141x^14+188x^15+251x^16+296x^17+357x^18+484x^19+466x^20+540x^21+378x^22+324x^23+242x^24+152x^25+138x^26+28x^27+25x^28+6x^29+9x^30+2x^32+1x^34

The gray image is a code over GF(2) with n=40, k=12 and d=12.
This code was found by Heurico 1.16 in 0.28 seconds.