The generator matrix

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

generates a code of length 12 over Z4 who´s minimum homogenous weight is 5.

Homogenous weight enumerator: w(x)=1x^0+44x^5+158x^6+350x^7+685x^8+1252x^9+1937x^10+2434x^11+2651x^12+2488x^13+1877x^14+1218x^15+750x^16+372x^17+123x^18+30x^19+9x^20+4x^21+1x^22

The gray image is a code over GF(2) with n=24, k=14 and d=5.
This code was found by Heurico 1.10 in 0.115 seconds.