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 2
0 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

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

Homogenous weight enumerator: w(x)=1x^0+121x^4+82x^5+738x^6+936x^7+3158x^8+4888x^9+7428x^10+10488x^11+9870x^12+10460x^13+7448x^14+4888x^15+3129x^16+952x^17+764x^18+72x^19+105x^20+2x^21+6x^22

The gray image is a code over GF(2) with n=24, k=16 and d=4.
This code was found by Heurico 1.10 in 0.528 seconds.