The generator matrix

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

generates a code of length 87 over Z3[X]/(X^3) who´s minimum homogenous weight is 168.

Homogenous weight enumerator: w(x)=1x^0+192x^168+1596x^170+522x^171+72x^172+1260x^173+498x^174+72x^175+378x^176+416x^177+18x^178+1176x^179+200x^180+126x^182+22x^183+4x^186+2x^189+2x^198+2x^201+2x^207

The gray image is a linear code over GF(3) with n=783, k=8 and d=504.
This code was found by Heurico 1.16 in 0.44 seconds.