The generator matrix

 1  1  1  1  1  1  1  1  1  1  1  1  1  2  1  1  2  2  1  2
 0  2  0  0  0  0  0  0  0  0  0  0  0  2  0  2  2  0  2  2
 0  0  2  0  0  0  0  0  0  0  0  0  2  2  0  2  0  2  0  2
 0  0  0  2  0  0  0  0  0  0  0  0  2  0  2  2  2  2  2  2
 0  0  0  0  2  0  0  0  0  0  0  2  0  0  2  2  0  0  2  2
 0  0  0  0  0  2  0  0  0  0  0  2  0  2  0  0  2  2  2  0
 0  0  0  0  0  0  2  0  0  0  2  0  0  2  0  0  2  2  0  2
 0  0  0  0  0  0  0  2  0  0  2  0  0  0  2  2  2  0  2  0
 0  0  0  0  0  0  0  0  2  0  2  2  2  0  0  2  0  2  0  0
 0  0  0  0  0  0  0  0  0  2  2  2  2  2  2  0  0  2  0  2

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

Homogenous weight enumerator: w(x)=1x^0+101x^12+292x^16+256x^18+727x^20+256x^22+340x^24+67x^28+7x^32+1x^36

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 0.0776 seconds.