The generator matrix

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

generates a code of length 36 over Z3[X]/(X^2) who´s minimum homogenous weight is 68.

Homogenous weight enumerator: w(x)=1x^0+186x^68+96x^69+126x^71+74x^72+54x^74+52x^75+84x^77+6x^78+18x^80+18x^83+14x^84

The gray image is a linear code over GF(3) with n=108, k=6 and d=68.
This code was found by Heurico 1.16 in 0.037 seconds.