The generator matrix

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

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+360x^167+1514x^168+720x^170+1380x^171+216x^173+518x^174+504x^176+1076x^177+144x^179+114x^180+4x^183+6x^189+2x^204+2x^207

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 36.7 seconds.