The generator matrix

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

generates a code of length 77 over Z3[X]/(X^3) who´s minimum homogenous weight is 143.

Homogenous weight enumerator: w(x)=1x^0+402x^143+1034x^144+1776x^145+3936x^146+5032x^147+5652x^148+7950x^149+11458x^150+10410x^151+13536x^152+17086x^153+15336x^154+16884x^155+17748x^156+12870x^157+12294x^158+9690x^159+5370x^160+4044x^161+2354x^162+936x^163+540x^164+344x^165+96x^166+84x^167+86x^168+24x^169+72x^170+36x^171+6x^172+24x^173+6x^174+12x^175+12x^176+6x^177

The gray image is a linear code over GF(3) with n=693, k=11 and d=429.
This code was found by Heurico 1.16 in 82.1 seconds.