The generator matrix

 1  1  1  1  1  1  1  1  1  1  1  1  1  1  X 2X^2  X  1
 0  X  0  0 2X^2  X 2X^2+X  X 2X^2 2X^2+X 2X^2+2X X^2+2X  0  X 2X^2  0 2X X^2+2X
 0  0  X  0 2X^2+X 2X 2X X^2 2X X^2+X  X X^2+2X X^2 X^2 2X  X 2X^2+X X^2+2X
 0  0  0  X 2X^2+2X X^2+X X^2+2X 2X^2+X 2X^2 2X^2+X  X X^2 2X^2+2X 2X^2+2X  0 X^2+X X^2+X X^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+216x^29+244x^30+276x^31+840x^32+574x^33+2334x^34+2076x^35+4844x^36+4248x^37+2232x^38+728x^39+408x^40+420x^41+164x^42+24x^43+48x^44+6x^45

The gray image is a linear code over GF(3) with n=162, k=9 and d=87.
This code was found by Heurico 1.16 in 0.613 seconds.