The generator matrix

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

generates a code of length 12 over Z4 who´s minimum homogenous weight is 7.

Homogenous weight enumerator: w(x)=1x^0+60x^7+129x^8+146x^9+222x^10+294x^11+301x^12+324x^13+276x^14+152x^15+78x^16+42x^17+14x^18+6x^19+3x^20

The gray image is a code over GF(2) with n=24, k=11 and d=7.
This code was found by Heurico 1.10 in 0.047 seconds.