The generator matrix

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

generates a code of length 11 over Z4 who´s minimum homogenous weight is 7.

Homogenous weight enumerator: w(x)=1x^0+24x^7+60x^8+64x^9+74x^10+80x^11+60x^12+64x^13+52x^14+24x^15+7x^16+2x^18

The gray image is a code over GF(2) with n=22, k=9 and d=7.
This code was found by Heurico 1.10 in 0 seconds.