The generator matrix

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

generates a code of length 86 over Z3[X]/(X^3) who´s minimum homogenous weight is 168.

Homogenous weight enumerator: w(x)=1x^0+42x^168+36x^169+54x^170+80x^171+1710x^172+108x^173+114x^174+36x^175+4x^177+2x^258

The gray image is a linear code over GF(3) with n=774, k=7 and d=504.
This code was found by Heurico 1.16 in 0.293 seconds.