The generator matrix

 1  0  0  1  1  1  1  1  1 2X^2+2X  1  1  1  1  1  1  1  1
 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 X^2+2X X^2+1 2X^2+X+2 2X+2
 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^2 X^2+2 X^2+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+306x^31+720x^32+1342x^33+2052x^34+2556x^35+4530x^36+3636x^37+2718x^38+1320x^39+468x^40+14x^42+18x^43+2x^45

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 0.21 seconds.