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

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+234x^67+318x^68+374x^69+690x^70+840x^71+682x^72+1008x^73+1116x^74+854x^75+1422x^76+1470x^77+1146x^78+1440x^79+1692x^80+1096x^81+1302x^82+1182x^83+684x^84+900x^85+570x^86+202x^87+264x^88+96x^89+46x^90+30x^91+6x^92+8x^93+4x^96+2x^99+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 6.86 seconds.