The generator matrix

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

generates a code of length 20 over Z4 who´s minimum homogenous weight is 12.

Homogenous weight enumerator: w(x)=1x^0+51x^12+32x^13+114x^14+128x^15+191x^16+320x^17+404x^18+544x^19+522x^20+544x^21+392x^22+320x^23+222x^24+128x^25+108x^26+32x^27+35x^28+6x^30+2x^32

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 0.242 seconds.