The generator matrix
1 1 1 1 1 1
0 3 0 0 3 0
0 0 3 0 6 0
0 0 0 3 6 0
generates a code of length 6 over Z9 who´s minimum homogenous weight is 6.
Homogenous weight enumerator: w(x)=1x^0+12x^6+16x^9+180x^12+24x^15+10x^18
The gray image is a code over GF(3) with n=18, k=5 and d=6.
This code was found by Heurico 1.16 in 7.7e-005 seconds.