The generator matrix

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

generates a code of length 10 over Z4 who´s minimum homogenous weight is 6.

Homogenous weight enumerator: w(x)=1x^0+32x^6+48x^7+51x^8+80x^9+77x^10+80x^11+74x^12+48x^13+18x^14+2x^16+1x^18

The gray image is a code over GF(2) with n=20, k=9 and d=6.
This code was found by Heurico 1.10 in 0 seconds.