The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+85x^4+52x^5+597x^6+444x^7+2034x^8+2452x^9+3532x^10+5244x^11+3874x^12+5244x^13+3566x^14+2452x^15+1997x^16+444x^17+620x^18+52x^19+73x^20+5x^22

The gray image is a code over GF(2) with n=24, k=15 and d=4.
This code was found by Heurico 1.10 in 0.101 seconds.