The generator matrix

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

generates a code of length 18 over Z3[X]/(X^3) who´s minimum homogenous weight is 29.

Homogenous weight enumerator: w(x)=1x^0+390x^29+1780x^30+1404x^31+7464x^32+6378x^33+19602x^34+27678x^35+35284x^36+36288x^37+27690x^38+9610x^39+2484x^40+852x^41+156x^42+78x^44+4x^45+4x^48

The gray image is a linear code over GF(3) with n=162, k=11 and d=87.
This code was found by Heurico 1.16 in 126 seconds.