The generator matrix

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

generates a code of length 36 over Z3[X]/(X^2) who´s minimum homogenous weight is 64.

Homogenous weight enumerator: w(x)=1x^0+252x^64+474x^65+136x^66+552x^67+498x^68+196x^69+600x^70+624x^71+104x^72+564x^73+582x^74+162x^75+522x^76+450x^77+72x^78+318x^79+222x^80+48x^81+102x^82+60x^83+8x^84+6x^85+6x^86+2x^87

The gray image is a linear code over GF(3) with n=108, k=8 and d=64.
This code was found by Heurico 1.16 in 43 seconds.