The generator matrix

 1  0  0  1  1  1  1  1  1  1  1  1
 0  1  0 2X^2+2X+1  X 2X^2+X+1  1 2X^2+2X  2 2X^2+1 2X^2+2X  0
 0  0  1 2X^2+2X+2 X+2 2X^2+X  1 2X^2+2X+1 2X 2X^2 2X^2+X+2  0
 0  0  0 2X^2 X^2 2X^2  0 X^2 2X^2 X^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+276x^18+246x^19+1704x^20+1470x^21+6876x^22+6660x^23+19350x^24+13374x^25+6678x^26+1946x^27+402x^28+24x^29+42x^30

The gray image is a linear code over GF(3) with n=108, k=10 and d=54.
This code was found by Heurico 1.16 in 0.79 seconds.