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

generates a code of length 86 over Z3[X]/(X^3) who´s minimum homogenous weight is 162.

Homogenous weight enumerator: w(x)=1x^0+636x^162+1086x^165+216x^166+162x^167+1776x^168+1620x^169+810x^170+1626x^171+3402x^172+1782x^173+2398x^174+2052x^175+162x^176+696x^177+478x^180+346x^183+228x^186+146x^189+58x^192+2x^234

The gray image is a linear code over GF(3) with n=774, k=9 and d=486.
This code was found by Heurico 1.16 in 65 seconds.