The generator matrix
1 1 1 1 1 X 1 X 1
0 X 2X 0 X+3 X+3 2X X+3 0
0 0 6 0 0 3 3 6 0
0 0 0 6 0 3 0 6 3
0 0 0 0 3 3 6 0 6
generates a code of length 9 over Z9[X]/(X^2+3,3X) who´s minimum homogenous weight is 12.
Homogenous weight enumerator: w(x)=1x^0+54x^12+324x^14+180x^15+1296x^17+3156x^18+1296x^20+216x^21+36x^24+2x^27
The gray image is a code over GF(3) with n=81, k=8 and d=36.
This code was found by Heurico 1.16 in 0.0123 seconds.