The generator matrix

 1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1
 0  X 2X  0 2X^2+X 2X  0 2X^2+X 2X X^2 2X^2+X X^2+2X X^2 X^2+X  0 2X^2+X 2X^2  X
 0  0 X^2  0 X^2  0 2X^2 X^2 X^2 X^2 2X^2 2X^2 2X^2 X^2 X^2  0  0  0
 0  0  0 X^2 2X^2 X^2 X^2  0 X^2 X^2  0  0 2X^2 X^2  0 2X^2 2X^2 X^2

generates a code of length 18 over Z3[X]/(X^3) who´s minimum homogenous weight is 31.

Homogenous weight enumerator: w(x)=1x^0+84x^31+36x^33+156x^34+1644x^36+108x^37+114x^40+18x^42+24x^43+2x^54

The gray image is a linear code over GF(3) with n=162, k=7 and d=93.
This code was found by Heurico 1.16 in 0.362 seconds.