The generator matrix

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

generates a code of length 12 over Z4 who´s minimum homogenous weight is 6.

Homogenous weight enumerator: w(x)=1x^0+160x^6+682x^8+1928x^10+2672x^12+1872x^14+733x^16+136x^18+8x^20

The gray image is a code over GF(2) with n=24, k=13 and d=6.
This code was found by Heurico 1.10 in 0.0543 seconds.