The generator matrix

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

generates a code of length 76 over Z3[X]/(X^3) who´s minimum homogenous weight is 146.

Homogenous weight enumerator: w(x)=1x^0+1098x^146+1160x^147+1710x^148+2778x^149+1652x^150+1332x^151+2082x^152+1114x^153+1380x^154+1458x^155+870x^156+678x^157+978x^158+554x^159+228x^160+504x^161+70x^162+18x^163+12x^164+4x^165+2x^168

The gray image is a linear code over GF(3) with n=684, k=9 and d=438.
This code was found by Heurico 1.16 in 1.13 seconds.