The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+57x^12+30x^14+355x^16+260x^18+582x^20+416x^22+230x^24+60x^26+49x^28+2x^30+6x^32

The gray image is a code over GF(2) with n=40, k=11 and d=12.
This code was found by Heurico 1.16 in 0.0635 seconds.