The generator matrix
1 1 1 1 1 1 1 1 1
0 X 0 0 2X^2+X X 2X 2X^2+2X 2X
0 0 X 2X X^2+2X X 0 2X^2+X 2X
0 0 0 X^2 0 X^2 0 2X^2 2X^2
0 0 0 0 X^2 2X^2 X^2 2X^2 0
generates a code of length 9 over Z3[X]/(X^3) who´s minimum homogenous weight is 12.
Homogenous weight enumerator: w(x)=1x^0+252x^12+1368x^15+16224x^18+1800x^21+36x^24+2x^27
The gray image is a linear code over GF(3) with n=81, k=9 and d=36.
This code was found by Heurico 1.16 in 0.0908 seconds.