The generator matrix

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

generates a code of length 36 over Z3[X]/(X^2) who´s minimum homogenous weight is 63.

Homogenous weight enumerator: w(x)=1x^0+114x^63+138x^64+222x^65+648x^66+264x^67+294x^68+736x^69+288x^70+252x^71+704x^72+318x^73+318x^74+752x^75+258x^76+228x^77+450x^78+108x^79+126x^80+216x^81+66x^82+18x^83+22x^84+18x^85+2x^87

The gray image is a linear code over GF(3) with n=108, k=8 and d=63.
This code was found by Heurico 1.16 in 0.344 seconds.