The generator matrix

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

generates a code of length 18 over Z3[X]/(X^3) who´s minimum homogenous weight is 27.

Homogenous weight enumerator: w(x)=1x^0+104x^27+126x^30+450x^33+5142x^36+558x^39+90x^42+72x^45+18x^48

The gray image is a linear code over GF(3) with n=162, k=8 and d=81.
This code was found by Heurico 1.16 in 8.84 seconds.