The generator matrix

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

generates a code of length 78 over Z3[X]/(X^2) who´s minimum homogenous weight is 143.

Homogenous weight enumerator: w(x)=1x^0+402x^143+402x^144+1266x^146+660x^147+1776x^149+906x^150+1872x^152+952x^153+1710x^155+1004x^156+1776x^158+780x^159+1500x^161+766x^162+1470x^164+574x^165+894x^167+276x^168+312x^170+188x^171+126x^173+46x^174+18x^176+4x^180+2x^183

The gray image is a linear code over GF(3) with n=234, k=9 and d=143.
This code was found by Heurico 1.16 in 7.76 seconds.