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

generates a code of length 80 over Z3[X]/(X^3) who´s minimum homogenous weight is 153.

Homogenous weight enumerator: w(x)=1x^0+448x^153+36x^155+772x^156+648x^158+1120x^159+486x^160+1188x^161+1222x^162+72x^164+212x^165+146x^168+112x^171+60x^174+30x^177+6x^180+2x^225

The gray image is a linear code over GF(3) with n=720, k=8 and d=459.
This code was found by Heurico 1.16 in 0.865 seconds.