The generator matrix

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

generates a code of length 15 over Z3[X]/(X^3) who´s minimum homogenous weight is 18.

Homogenous weight enumerator: w(x)=1x^0+104x^18+210x^21+102x^24+338x^27+18102x^30+336x^33+276x^36+156x^39+48x^42+10x^45

The gray image is a linear code over GF(3) with n=135, k=9 and d=54.
This code was found by Heurico 1.16 in 0.251 seconds.