The generator matrix
1 1 1 1 1 1 1 1 1 1 1 1 1 X X 1 X 1
0 X 0 X^2 2X 2X^2+X X^2+X 2X^2+X 2X^2+2X 0 X X^2+2X X^2+2X 2X^2 2X^2+2X X^2+X X 2X^2+2X
0 0 X 2X^2+2X X^2 2X^2+2X X 0 X^2+X X^2 X^2+X X^2+X X^2+2X 2X X^2+X X^2+2X X X^2+2X
generates a code of length 18 over Z3[X]/(X^3) who´s minimum homogenous weight is 32.
Homogenous weight enumerator: w(x)=1x^0+180x^32+84x^33+252x^34+252x^35+564x^36+378x^37+306x^38+66x^39+72x^41+12x^42+18x^43+2x^45
The gray image is a linear code over GF(3) with n=162, k=7 and d=96.
This code was found by Heurico 1.16 in 42.8 seconds.