The generator matrix
1 1 1 1 1 1 1
0 3 0 0 3 0 3
0 0 3 0 6 3 6
0 0 0 3 6 6 3
generates a code of length 7 over Z9 who´s minimum homogenous weight is 9.
Homogenous weight enumerator: w(x)=1x^0+12x^9+22x^12+162x^14+30x^15+8x^18+8x^21
The gray image is a code over GF(3) with n=21, k=5 and d=9.
This code was found by Heurico 1.16 in 0.000168 seconds.