The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+113x^4+614x^6+1890x^8+3496x^10+4170x^12+3460x^14+1917x^16+616x^18+101x^20+6x^22

The gray image is a code over GF(2) with n=24, k=14 and d=4.
This code was found by Heurico 1.10 in 0.0421 seconds.