The generator matrix

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

generates a code of length 18 over Z3[X]/(X^3) who´s minimum homogenous weight is 28.

Homogenous weight enumerator: w(x)=1x^0+288x^28+828x^30+1260x^31+1782x^32+3276x^33+7596x^34+7128x^35+9420x^36+13104x^37+7128x^38+4500x^39+2358x^40+180x^42+180x^43+18x^48+2x^54

The gray image is a linear code over GF(3) with n=162, k=10 and d=84.
This code was found by Heurico 1.16 in 82.6 seconds.