The generator matrix

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

generates a code of length 81 over Z3[X]/(X^2) who´s minimum homogenous weight is 162.

Homogenous weight enumerator: w(x)=1x^0+236x^162+6x^189

The gray image is a linear code over GF(3) with n=243, k=5 and d=162.
As d=162 is an upper bound for linear (243,5,3)-codes, this code is optimal over Z3[X]/(X^2) for dimension 5.
This code was found by Heurico 1.16 in 0.0681 seconds.