The generator matrix

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

generates a code of length 9 over Z4 who´s minimum homogenous weight is 4.

Homogenous weight enumerator: w(x)=1x^0+59x^4+258x^6+715x^8+684x^10+277x^12+50x^14+4x^16

The gray image is a code over GF(2) with n=18, k=11 and d=4.
This code was found by Heurico 1.10 in 0 seconds.