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.