The generator matrix

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

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+104x^18+210x^21+102x^24+338x^27+4980x^30+336x^33+276x^36+156x^39+48x^42+10x^45

The gray image is a linear code over GF(3) with n=45, k=8 and d=18.
This code was found by Heurico 1.16 in 0.0719 seconds.