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

generates a code of length 80 over Z3[X]/(X^3) who´s minimum homogenous weight is 151.

Homogenous weight enumerator: w(x)=1x^0+54x^151+78x^152+32x^153+360x^154+192x^155+34x^156+78x^157+648x^158+60x^159+3006x^160+1338x^161+64x^162+174x^163+66x^164+36x^165+54x^166+12x^168+12x^169+42x^170+2x^171+114x^172+66x^173+30x^175+6x^178+2x^237

The gray image is a linear code over GF(3) with n=720, k=8 and d=453.
This code was found by Heurico 1.16 in 0.584 seconds.