The generator matrix

 1  1  1  1  1  1  1  X  1  1  X  X
 0  X  0  0 2X 2X^2+X  X 2X^2+X 2X^2+2X 2X 2X^2+X 2X^2+X
 0  0  X 2X  0 2X^2+2X X^2+X 2X^2+2X 2X^2+X X^2+2X 2X^2+2X X^2+2X
 0  0  0 X^2  0 2X^2 2X^2 2X^2 X^2  0 X^2  0
 0  0  0  0 X^2 X^2 2X^2  0 2X^2  0 X^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+624x^18+2268x^21+13446x^24+3176x^27+162x^30+6x^36

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 18.5 seconds.