The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+95x^12+104x^14+550x^16+648x^18+1267x^20+696x^22+560x^24+88x^26+77x^28+9x^32+1x^36

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 0.263 seconds.