The generator matrix

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

generates a code of length 27 over Z3[X]/(X^3) who´s minimum homogenous weight is 54.

Homogenous weight enumerator: w(x)=1x^0+726x^54+2x^81

The gray image is a linear code over GF(3) with n=243, k=6 and d=162.
As d=162 is an upper bound for linear (243,6,3)-codes, this code is optimal over Z3[X]/(X^3) for dimension 6.
This code was found by Heurico 1.16 in 1.35 seconds.