The generator matrix

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

generates a code of length 36 over Z3[X]/(X^2) who´s minimum homogenous weight is 72.

Homogenous weight enumerator: w(x)=1x^0+234x^72+8x^81

The gray image is a linear code over GF(3) with n=108, k=5 and d=72.
As d=72 is an upper bound for linear (108,5,3)-codes, this code is optimal over Z3[X]/(X^2) for dimension 5.
This code was found by Heurico 1.16 in 0.00591 seconds.