The generator matrix
1 1 1 1 1 1 1 1 1
0 X 0 0 0 X 0 2X 2X
0 0 X 0 0 2X X 0 2X
0 0 0 X 0 2X X 2X 0
0 0 0 0 X X X X 2X
generates a code of length 9 over Z3[X]/(X^2) who´s minimum homogenous weight is 12.
Homogenous weight enumerator: w(x)=1x^0+36x^12+72x^15+510x^18+72x^21+36x^24+2x^27
The gray image is a linear code over GF(3) with n=27, k=6 and d=12.
This code was found by Heurico 1.16 in 0.000717 seconds.