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

generates a code of length 67 over Z3[X]/(X^2) who´s minimum homogenous weight is 135.

Homogenous weight enumerator: w(x)=1x^0+74x^135+6x^144

The gray image is a linear code over GF(3) with n=201, k=4 and d=135.
As d=135 is an upper bound for linear (201,4,3)-codes, this code is optimal over Z3[X]/(X^2) for dimension 4.
This code was found by Heurico 1.16 in 0.0402 seconds.