The generator matrix

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

generates a code of length 40 over Z3[X]/(X^2) who´s minimum homogenous weight is 67.

Homogenous weight enumerator: w(x)=1x^0+252x^67+438x^68+540x^69+1038x^70+1338x^71+1162x^72+2316x^73+2574x^74+2194x^75+3282x^76+3792x^77+3046x^78+4182x^79+4932x^80+3246x^81+4836x^82+4428x^83+3024x^84+3900x^85+3024x^86+1444x^87+1620x^88+1164x^89+546x^90+390x^91+162x^92+90x^93+54x^94+18x^95+10x^96+2x^99+2x^102+2x^108

The gray image is a linear code over GF(3) with n=120, k=10 and d=67.
This code was found by Heurico 1.16 in 105 seconds.