The generator matrix

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

generates a code of length 11 over Z4 who´s minimum homogenous weight is 6.

Homogenous weight enumerator: w(x)=1x^0+184x^6+594x^8+1248x^10+1304x^12+600x^14+149x^16+16x^18

The gray image is a code over GF(2) with n=22, k=12 and d=6.
This code was found by Heurico 1.10 in 0.016 seconds.