The generator matrix

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

generates a code of length 12 over Z4 who´s minimum homogenous weight is 4.

Homogenous weight enumerator: w(x)=1x^0+51x^4+314x^6+959x^8+1702x^10+2138x^12+1702x^14+959x^16+314x^18+51x^20+1x^24

The gray image is a code over GF(2) with n=24, k=13 and d=4.
This code was found by Heurico 1.10 in 0.0163 seconds.