The generator matrix

 1  1  1  1  1  1  1  1  1  X  X  X
 0 X^2  0  0  0  0  0 X^2 X^2 X^2 X^2 X^2
 0  0 X^2  0  0  0 X^2 2X^2 2X^2 X^2 X^2  0
 0  0  0 X^2  0  0 2X^2 2X^2 X^2  0 X^2 2X^2
 0  0  0  0 X^2  0 2X^2 X^2 2X^2 X^2  0 2X^2
 0  0  0  0  0 X^2 X^2  0 X^2 X^2 2X^2 2X^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+318x^18+324x^21+5022x^24+872x^27+24x^36

The gray image is a linear code over GF(3) with n=108, k=8 and d=54.
This code was found by Heurico 1.16 in 0.0273 seconds.