The generator matrix

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

generates a code of length 86 over Z3[X]/(X^3) who´s minimum homogenous weight is 167.

Homogenous weight enumerator: w(x)=1x^0+678x^167+526x^168+744x^169+948x^170+512x^171+456x^172+612x^173+340x^174+432x^175+462x^176+222x^177+144x^178+330x^179+86x^180+42x^182+6x^184+6x^188+2x^189+8x^192+2x^198+2x^204

The gray image is a linear code over GF(3) with n=774, k=8 and d=501.
This code was found by Heurico 1.16 in 376 seconds.