The generator matrix

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

generates a code of length 12 over Z4 who´s minimum homogenous weight is 3.

Homogenous weight enumerator: w(x)=1x^0+20x^3+91x^4+272x^5+733x^6+1728x^7+3274x^8+5280x^9+7492x^10+9064x^11+9574x^12+9120x^13+7526x^14+5280x^15+3237x^16+1696x^17+756x^18+292x^19+79x^20+16x^21+5x^22

The gray image is a code over GF(2) with n=24, k=16 and d=3.
This code was found by Heurico 1.10 in 0.246 seconds.