The generator matrix

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

generates a code of length 12 over Z4 who´s minimum homogenous weight is 8.

Homogenous weight enumerator: w(x)=1x^0+22x^8+72x^9+91x^10+56x^11+24x^12+56x^13+99x^14+72x^15+17x^16+1x^18+1x^22

The gray image is a code over GF(2) with n=24, k=9 and d=8.
This code was found by Heurico 1.10 in 0 seconds.