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

generates a code of length 85 over Z3[X]/(X^3) who´s minimum homogenous weight is 166.

Homogenous weight enumerator: w(x)=1x^0+36x^166+84x^168+144x^169+1620x^170+152x^171+144x^172+4x^174+2x^255

The gray image is a linear code over GF(3) with n=765, k=7 and d=498.
This code was found by Heurico 1.16 in 0.281 seconds.