The generator matrix

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

generates a code of length 15 over Z3[X]/(X^2) who´s minimum homogenous weight is 18.

Homogenous weight enumerator: w(x)=1x^0+76x^18+486x^21+486x^22+1680x^24+3888x^25+4058x^27+11664x^28+6372x^30+15552x^31+5064x^33+7776x^34+1776x^36+108x^39+60x^42+2x^45

The gray image is a linear code over GF(3) with n=45, k=10 and d=18.
This code was found by Heurico 1.16 in 3 seconds.