The generator matrix

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

generates a code of length 12 over Z4 who´s minimum homogenous weight is 6.

Homogenous weight enumerator: w(x)=1x^0+39x^6+68x^7+87x^8+148x^9+219x^10+296x^11+337x^12+296x^13+213x^14+148x^15+84x^16+68x^17+41x^18+3x^20

The gray image is a code over GF(2) with n=24, k=11 and d=6.
This code was found by Heurico 1.16 in 0.0127 seconds.