The generator matrix

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

generates a code of length 39 over Z3[X]/(X^2) who´s minimum homogenous weight is 67.

Homogenous weight enumerator: w(x)=1x^0+216x^67+348x^68+440x^69+660x^70+666x^71+716x^72+1014x^73+1290x^74+800x^75+1428x^76+1524x^77+1040x^78+1488x^79+1638x^80+1074x^81+1386x^82+1104x^83+684x^84+858x^85+630x^86+294x^87+192x^88+90x^89+36x^90+48x^91+8x^93+6x^96+2x^102+2x^105

The gray image is a linear code over GF(3) with n=117, k=9 and d=67.
This code was found by Heurico 1.16 in 14.2 seconds.