The generator matrix

 1  0  0  1  1  1  0  1  1  1  1  1
 0  1  0  1  0  1  1  0  0  0  0  0
 0  0  1  1  1  0  1  0  0  0  0  0
 0  0  0  2  0  0  0  0  0  0  2  0
 0  0  0  0  2  0  0  0  0  0  2  0
 0  0  0  0  0  2  0  0  0  0  2  0
 0  0  0  0  0  0  2  0  0  0  2  0
 0  0  0  0  0  0  0  2  0  0  2  0
 0  0  0  0  0  0  0  0  2  0  2  0
 0  0  0  0  0  0  0  0  0  2  2  0

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

Homogenous weight enumerator: w(x)=1x^0+69x^4+154x^6+594x^8+512x^9+744x^10+1536x^11+930x^12+1536x^13+876x^14+512x^15+429x^16+264x^18+25x^20+10x^22

The gray image is a code over GF(2) with n=24, k=13 and d=4.
This code was found by Heurico 1.16 in 0.126 seconds.