The generator matrix

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

generates a code of length 88 over Z3[X]/(X^3) who´s minimum homogenous weight is 171.

Homogenous weight enumerator: w(x)=1x^0+530x^171+750x^172+972x^173+986x^174+582x^175+300x^177+666x^178+552x^180+402x^181+486x^182+292x^183+30x^184+2x^186+4x^189+2x^198+2x^204+2x^213

The gray image is a linear code over GF(3) with n=792, k=8 and d=513.
This code was found by Heurico 1.16 in 0.483 seconds.