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  X  1
 0  X 2X  0 2X^2+X 2X 2X^2+X X^2+2X  0 X^2 2X^2+X 2X  0 X^2+X 2X^2+2X X^2 2X^2+X X^2+2X X^2  X X^2 X^2+2X  X X^2+2X 2X^2  X 2X  0  0 X^2 X^2 2X^2+X 2X^2+X  X  X 2X X^2+2X 2X X^2+2X X^2+X X^2 2X 2X^2+X 2X^2+2X 2X^2 2X^2 X^2 X^2+X 2X^2+2X 2X^2+X 2X  0  X X^2+2X 2X^2 X^2+X 2X^2+2X  0  X 2X^2 X^2+2X 2X^2+2X 2X^2+2X X^2+X X^2+X  0 X^2 2X^2 X^2+X X^2+X 2X X^2+2X 2X^2 2X^2 2X^2 2X^2+X X^2+X  X 2X^2+2X 2X^2+2X 2X^2+2X  0 2X^2+X 2X 2X^2+X  0
 0  0 X^2  0 2X^2  0 X^2 2X^2 X^2 2X^2 2X^2  0 X^2 2X^2 2X^2  0  0 2X^2 2X^2 X^2 X^2 X^2 X^2  0 2X^2  0 X^2  0 X^2 2X^2 X^2 2X^2 X^2 2X^2 2X^2 2X^2 X^2 2X^2  0  0  0 2X^2 X^2 X^2 2X^2 X^2  0  0  0  0 X^2 2X^2 X^2  0  0 2X^2  0 2X^2 2X^2 X^2 2X^2 X^2 2X^2 X^2 X^2 2X^2 X^2  0 X^2 2X^2  0 X^2  0 X^2 2X^2  0  0  0  0 X^2 2X^2  0 2X^2  0 2X^2 X^2
 0  0  0 X^2 X^2 X^2 2X^2 2X^2 2X^2 X^2 2X^2 2X^2  0  0 X^2 2X^2 X^2  0 2X^2 X^2 X^2 2X^2  0  0  0 2X^2 X^2 2X^2 X^2  0  0  0  0 X^2 2X^2 2X^2 X^2  0 X^2 X^2  0 X^2 X^2  0 X^2 2X^2 X^2  0  0 2X^2 2X^2 2X^2 2X^2 2X^2 2X^2 X^2 X^2 X^2  0  0 X^2 2X^2 2X^2  0 X^2  0 2X^2 X^2 2X^2 2X^2  0  0  0 X^2 2X^2  0 2X^2 X^2 2X^2 X^2  0  0 2X^2  0 X^2  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+38x^168+324x^170+92x^171+972x^172+648x^173+100x^174+10x^177+2x^255

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 0.385 seconds.