The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+26x^5+71x^6+170x^7+359x^8+610x^9+959x^10+1250x^11+1317x^12+1230x^13+957x^14+606x^15+364x^16+182x^17+61x^18+22x^19+7x^20

The gray image is a code over GF(2) with n=24, k=13 and d=5.
This code was found by Heurico 1.10 in 0.0306 seconds.