The generator matrix

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

generates a code of length 38 over Z3[X]/(X^2) who´s minimum homogenous weight is 65.

Homogenous weight enumerator: w(x)=1x^0+222x^65+288x^66+294x^67+750x^68+770x^69+624x^70+1248x^71+1116x^72+690x^73+1806x^74+1256x^75+1104x^76+1728x^77+1278x^78+804x^79+1728x^80+1224x^81+600x^82+1032x^83+534x^84+222x^85+204x^86+76x^87+30x^88+30x^89+8x^90+6x^91+10x^93

The gray image is a linear code over GF(3) with n=114, k=9 and d=65.
This code was found by Heurico 1.16 in 3.62 seconds.