The generator matrix

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

generates a code of length 40 over Z3[X]/(X^2) who´s minimum homogenous weight is 81.

Homogenous weight enumerator: w(x)=1x^0+80x^81

The gray image is a linear code over GF(3) with n=120, k=4 and d=81.
As d=81 is an upper bound for linear (120,4,3)-codes, this code is optimal over Z3[X]/(X^2) for dimension 4.
This code was found by Heurico 1.13 in 0.00651 seconds.