The generator matrix

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

generates a code of length 10 over Z4 who´s minimum homogenous weight is 8.

Homogenous weight enumerator: w(x)=1x^0+130x^8+120x^12+5x^16

The gray image is a code over GF(2) with n=20, k=8 and d=8.
This code was found by Heurico 1.10 in 0.172 seconds.