The generator matrix

 1  1  1  1  1  1  1  X  X  1  1  1
 0  X 2X  0 2X^2+X 2X  0 2X^2+X 2X  0 X^2 X^2
 0  0 X^2  0  0 X^2 X^2 2X^2  0 X^2 2X^2 2X^2
 0  0  0 X^2  0 2X^2 X^2 X^2 2X^2  0 2X^2 2X^2
 0  0  0  0 2X^2 2X^2  0 2X^2 2X^2 X^2 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+108x^18+162x^20+168x^21+972x^22+648x^23+1638x^24+1944x^25+648x^26+152x^27+120x^30

The gray image is a linear code over GF(3) with n=108, k=8 and d=54.
This code was found by Heurico 1.16 in 0.026 seconds.