The generator matrix
1 1 1 1 1 1 1 1 1
0 3 0 0 0 3 0 6 6
0 0 3 0 0 6 3 0 6
0 0 0 3 0 6 3 6 0
0 0 0 0 3 3 3 3 6
generates a code of length 9 over Z9[X]/(X^2+6,3X) who´s minimum homogenous weight is 12.
Homogenous weight enumerator: w(x)=1x^0+36x^12+72x^15+1968x^18+72x^21+36x^24+2x^27
The gray image is a code over GF(3) with n=81, k=7 and d=36.
This code was found by Heurico 1.16 in 0.00209 seconds.