The generator matrix

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

generates a code of length 54 over Z3[X]/(X^2) who´s minimum homogenous weight is 108.

Homogenous weight enumerator: w(x)=1x^0+74x^108+6x^126

The gray image is a linear code over GF(3) with n=162, k=4 and d=108.
As d=108 is an upper bound for linear (162,4,3)-codes, this code is optimal over Z3[X]/(X^2) for dimension 4.
This code was found by Heurico 1.16 in 0.0181 seconds.