The generator matrix

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

generates a code of length 40 over Z3[X]/(X^2) who´s minimum homogenous weight is 65.

Homogenous weight enumerator: w(x)=1x^0+474x^65+462x^66+2628x^68+1864x^69+6462x^71+4154x^72+12834x^74+7908x^75+21198x^77+11806x^78+27240x^80+13544x^81+24678x^83+11172x^84+15042x^86+5844x^87+5982x^89+1920x^90+1380x^92+324x^93+174x^95+32x^96+6x^98+10x^99+6x^102+2x^105

The gray image is a linear code over GF(3) with n=120, k=11 and d=65.
This code was found by Heurico 1.16 in 429 seconds.