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  0  1  1  1  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  X X+2 2X 2X+2 2X+1  X
 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  X  1  1  0  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  2  0  2 X+2  X X+1
 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 X+2  X  X X+2 2X 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+258x^67+258x^68+724x^69+1302x^70+810x^71+1766x^72+2334x^73+1584x^74+2660x^75+4074x^76+2250x^77+3840x^78+5466x^79+2826x^80+4018x^81+6042x^82+2802x^83+3576x^84+4428x^85+1824x^86+2244x^87+1890x^88+648x^89+704x^90+390x^91+114x^92+114x^93+60x^94+6x^95+32x^96+4x^102

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 31.1 seconds.