The generator matrix

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

generates a code of length 18 over Z3[X]/(X^3) who´s minimum homogenous weight is 35.

Homogenous weight enumerator: w(x)=1x^0+324x^35+240x^36+162x^38+2x^54

The gray image is a linear code over GF(3) with n=162, k=6 and d=105.
As d=106 is an upper bound for linear (162,6,3)-codes, this code is optimal over Z3[X]/(X^3) for dimension 6.
This code was found by Heurico 1.16 in 0.133 seconds.