The generator matrix

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

generates a code of length 39 over Z3[X]/(X^2) who´s minimum homogenous weight is 65.

Homogenous weight enumerator: w(x)=1x^0+246x^65+402x^66+612x^67+1086x^68+1176x^69+1230x^70+2064x^71+2248x^72+2502x^73+3480x^74+3348x^75+3264x^76+4326x^77+4588x^78+4290x^79+4896x^80+4170x^81+3294x^82+3642x^83+2638x^84+1734x^85+1620x^86+924x^87+474x^88+456x^89+176x^90+90x^91+48x^92+2x^93+6x^94+6x^95+6x^96+2x^99+2x^114

The gray image is a linear code over GF(3) with n=117, k=10 and d=65.
This code was found by Heurico 1.16 in 26 seconds.