The generator matrix

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

generates a code of length 46 over Z3[X]/(X^2) who´s minimum homogenous weight is 82.

Homogenous weight enumerator: w(x)=1x^0+96x^82+156x^83+230x^84+378x^85+174x^86+420x^87+558x^88+318x^89+454x^90+618x^91+216x^92+410x^93+444x^94+258x^95+260x^96+462x^97+192x^98+286x^99+252x^100+96x^101+76x^102+96x^103+36x^104+38x^105+6x^106+12x^107+6x^108+6x^109+2x^111+2x^114+2x^120

The gray image is a linear code over GF(3) with n=138, k=8 and d=82.
This code was found by Heurico 1.16 in 0.44 seconds.