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

generates a code of length 77 over Z3[X]/(X^3) who´s minimum homogenous weight is 144.

Homogenous weight enumerator: w(x)=1x^0+498x^144+1110x^147+54x^148+72x^149+1788x^150+324x^151+1404x^152+3698x^153+2106x^154+2808x^155+3402x^156+432x^157+90x^158+666x^159+554x^162+300x^165+228x^168+116x^171+30x^174+2x^216

The gray image is a linear code over GF(3) with n=693, k=9 and d=432.
This code was found by Heurico 1.16 in 2.9 seconds.