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

generates a code of length 69 over Z3[X]/(X^2) who´s minimum homogenous weight is 138.

Homogenous weight enumerator: w(x)=1x^0+66x^138+4x^144+6x^147+4x^153

The gray image is a linear code over GF(3) with n=207, k=4 and d=138.
As d=138 is an upper bound for linear (207,4,3)-codes, this code is optimal over Z3[X]/(X^2) for dimension 4.
This code was found by Heurico 1.16 in 0.0495 seconds.