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

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+630x^167+622x^168+660x^169+942x^170+628x^171+492x^172+540x^173+338x^174+288x^175+438x^176+348x^177+174x^178+324x^179+74x^180+36x^182+6x^184+6x^186+6x^191+2x^192+2x^195+2x^198+2x^201

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 2.06 seconds.