The generator matrix

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

generates a code of length 36 over Z3[X]/(X^2) who´s minimum homogenous weight is 69.

Homogenous weight enumerator: w(x)=1x^0+432x^69+72x^72+216x^78+8x^81

The gray image is a linear code over GF(3) with n=108, k=6 and d=69.
As d=69 is an upper bound for linear (108,6,3)-codes, this code is optimal over Z3[X]/(X^2) for dimension 6.
This code was found by Heurico 1.16 in 0.0123 seconds.