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

generates a code of length 48 over Z3[X]/(X^2) who´s minimum homogenous weight is 96.

Homogenous weight enumerator: w(x)=1x^0+60x^96+12x^99+6x^102+2x^108

The gray image is a linear code over GF(3) with n=144, k=4 and d=96.
As d=96 is an upper bound for linear (144,4,3)-codes, this code is optimal over Z3[X]/(X^2) for dimension 4.
This code was found by Heurico 1.16 in 0.013 seconds.