The generator matrix

 1  0  1  1  1  1  1 2X^2+X  1  1  1  0
 0  1 2X^2+2X+1  2 2X^2+X X+1 2X^2+X+2  1 2X 2X^2+1  2  1
 0  0 2X^2  0  0  0 2X^2 2X^2  0 X^2 X^2 X^2
 0  0  0 X^2  0  0 2X^2 2X^2 X^2 2X^2  0 2X^2
 0  0  0  0 2X^2  0 X^2 2X^2 X^2  0 2X^2 X^2
 0  0  0  0  0 X^2 2X^2  0 2X^2 2X^2 2X^2 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+480x^18+972x^20+1296x^21+11664x^22+3888x^23+11340x^24+23328x^25+3888x^26+2168x^27+24x^36

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 0.692 seconds.