The generator matrix

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

generates a code of length 12 over Z3[X]/(X^3) who´s minimum homogenous weight is 18.

Homogenous weight enumerator: w(x)=1x^0+162x^18+324x^20+492x^21+3402x^22+1296x^23+5202x^24+6804x^25+1296x^26+584x^27+120x^30

The gray image is a linear code over GF(3) with n=108, k=9 and d=54.
This code was found by Heurico 1.16 in 0.118 seconds.