The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+61x^6+92x^7+185x^8+312x^9+425x^10+588x^11+651x^12+688x^13+503x^14+276x^15+186x^16+88x^17+35x^18+4x^19+1x^20

The gray image is a code over GF(2) with n=24, k=12 and d=6.
This code was found by Heurico 1.10 in 0.031 seconds.