The generator matrix

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

generates a code of length 11 over Z4 who´s minimum homogenous weight is 8.

Homogenous weight enumerator: w(x)=1x^0+170x^8+296x^12+45x^16

The gray image is a code over GF(2) with n=22, k=9 and d=8.
This code was found by an older version of Heurico in 0 seconds.