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

generates a code of length 76 over Z3[X]/(X^3) who´s minimum homogenous weight is 144.

Homogenous weight enumerator: w(x)=1x^0+166x^144+528x^147+2148x^150+3120x^153+240x^156+78x^159+32x^162+204x^165+42x^168+2x^225

The gray image is a linear code over GF(3) with n=684, k=8 and d=432.
This code was found by Heurico 1.16 in 0.52 seconds.