The generator matrix

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

generates a code of length 68 over Z3[X]/(X^2) who´s minimum homogenous weight is 136.

Homogenous weight enumerator: w(x)=1x^0+54x^136+12x^138+8x^141+2x^144+4x^150

The gray image is a linear code over GF(3) with n=204, k=4 and d=136.
As d=136 is an upper bound for linear (204,4,3)-codes, this code is optimal over Z3[X]/(X^2) for dimension 4.
This code was found by Heurico 1.16 in 0.0338 seconds.