The generator matrix

1 0 0 0 0 0 1 1 1
0 1 0 0 0 0 1 0 0
0 0 1 0 0 0 1 0 0
0 0 0 1 0 0 1 0 0
0 0 0 0 1 0 1 0 0
0 0 0 0 0 1 1 0 0
0 0 0 0 0 0 2 0 0

generates a code of length 9 over Z4 who´s minimum homogenous weight is 2.

Homogenous weight enumerator: w(x)=1x^0+66x^2+519x^4+1365x^6+2145x^8+2145x^10+1365x^12+519x^14+66x^16+1x^18

The gray image is a code over GF(2) with n=18, k=13 and d=2.
This code was found by Heurico 1.10 in 0.000584 seconds.