The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+446x^12+1410x^14+3530x^16+6920x^18+8212x^20+6684x^22+3840x^24+1320x^26+350x^28+50x^30+5x^32

The gray image is a code over GF(2) with n=40, k=15 and d=12.
This code was found by Heurico 1.16 in 49.9 seconds.