The generator matrix

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

generates a code of length 18 over Z3[X]/(X^3) who´s minimum homogenous weight is 29.

Homogenous weight enumerator: w(x)=1x^0+198x^29+694x^30+708x^31+2172x^32+2500x^33+7518x^34+7242x^35+11270x^36+13968x^37+7434x^38+3626x^39+1110x^40+384x^41+128x^42+24x^43+66x^44+6x^45

The gray image is a linear code over GF(3) with n=162, k=10 and d=87.
This code was found by Heurico 1.16 in 10.9 seconds.