The generator matrix

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

generates a code of length 18 over Z3[X]/(X^3) who´s minimum homogenous weight is 36.

Homogenous weight enumerator: w(x)=1x^0+74x^36+6x^42

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^3) for dimension 4.
This code was found by Heurico 1.16 in 0.000878 seconds.