The generator matrix

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

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+24x^18+54x^22+522x^24+108x^25+2x^27+18x^33

The gray image is a linear code over GF(3) with n=108, k=6 and d=54.
This code was found by Heurico 1.16 in 0.000837 seconds.