The generator matrix

 1  1  1  1  1  1  1  1  1
 0  X 2X  0 2X^2+X  0 2X^2+X X^2 2X^2+X
 0  0 X^2  0 X^2 X^2 X^2 2X^2  0
 0  0  0 X^2 2X^2 2X^2  0 2X^2 2X^2

generates a code of length 9 over Z3[X]/(X^3) who´s minimum homogenous weight is 13.

Homogenous weight enumerator: w(x)=1x^0+48x^13+36x^15+126x^16+1644x^18+252x^19+60x^22+18x^24+2x^27

The gray image is a linear code over GF(3) with n=81, k=7 and d=39.
This code was found by Heurico 1.16 in 0.01 seconds.