The generator matrix

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

generates a code of length 80 over Z3[X]/(X^3) who´s minimum homogenous weight is 154.

Homogenous weight enumerator: w(x)=1x^0+84x^154+540x^155+940x^156+36x^157+1188x^158+822x^159+216x^160+756x^161+80x^162+120x^163+702x^164+732x^165+18x^166+216x^167+92x^168+12x^172+2x^183+4x^195

The gray image is a linear code over GF(3) with n=720, k=8 and d=462.
This code was found by Heurico 1.16 in 0.351 seconds.