The generator matrix

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

generates a code of length 39 over Z3[X]/(X^2) who´s minimum homogenous weight is 64.

Homogenous weight enumerator: w(x)=1x^0+84x^64+282x^65+360x^66+378x^67+1314x^68+1162x^69+960x^70+2334x^71+2322x^72+1770x^73+3978x^74+3466x^75+2718x^76+5556x^77+4476x^78+2952x^79+6090x^80+4140x^81+2358x^82+4242x^83+2652x^84+1434x^85+1986x^86+912x^87+408x^88+378x^89+130x^90+54x^91+84x^92+30x^93+6x^94+20x^96+4x^99+8x^102

The gray image is a linear code over GF(3) with n=117, k=10 and d=64.
This code was found by Heurico 1.16 in 24.6 seconds.