The generator matrix

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

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+252x^31+918x^32+1184x^33+1668x^34+3300x^35+4508x^36+2832x^37+3336x^38+1188x^39+420x^40+60x^41+4x^42+12x^43

The gray image is a linear code over GF(3) with n=162, k=9 and d=93.
This code was found by Heurico 1.16 in 0.242 seconds.