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

generates a code of length 77 over Z3[X]/(X^2) who´s minimum homogenous weight is 155.

Homogenous weight enumerator: w(x)=1x^0+54x^155+12x^156+12x^159+2x^162

The gray image is a linear code over GF(3) with n=231, k=4 and d=155.
As d=155 is an upper bound for linear (231,4,3)-codes, this code is optimal over Z3[X]/(X^2) for dimension 4.
This code was found by Heurico 1.13 in 0.0838 seconds.