The generator matrix

 1  0  1  1  1  1 2X^2  1  1  1  1  X
 0  1  1  2 2X^2+2X+1 2X^2  1 2X^2+X+2 2X^2+2X+1 2X^2+1 2X+1 2X^2
 0  0 2X  0  0 2X^2+X 2X^2+X 2X^2 2X^2+2X 2X^2  X 2X^2+X
 0  0  0 X^2  0 2X^2 X^2  0 2X^2 X^2  0 2X^2
 0  0  0  0 2X^2 2X^2  0 2X^2  0 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+822x^18+1458x^20+2178x^21+7290x^22+5832x^23+17388x^24+14580x^25+5832x^26+3518x^27+144x^30+6x^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 24.7 seconds.