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

generates a code of length 76 over Z3[X]/(X^3) who´s minimum homogenous weight is 145.

Homogenous weight enumerator: w(x)=1x^0+198x^145+336x^146+70x^147+408x^148+528x^149+570x^150+822x^151+792x^152+996x^153+750x^154+594x^155+22x^156+42x^157+48x^158+18x^159+120x^160+48x^161+2x^162+54x^163+72x^164+12x^165+18x^166+6x^168+12x^169+6x^170+6x^172+6x^173+2x^174+2x^210

The gray image is a linear code over GF(3) with n=684, k=8 and d=435.
This code was found by Heurico 1.16 in 21.9 seconds.