The generator matrix

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

generates a code of length 31 over Z3[X]/(X^2) who´s minimum homogenous weight is 60.

Homogenous weight enumerator: w(x)=1x^0+114x^60+94x^63+18x^66+12x^69+4x^72

The gray image is a linear code over GF(3) with n=93, k=5 and d=60.
As d=60 is an upper bound for linear (93,5,3)-codes, this code is optimal over Z3[X]/(X^2) for dimension 5.
This code was found by Heurico 1.16 in 0.00388 seconds.