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  X  X  X  X  X  X  X  X  X  X  X  X  X  X  X  X  X  X  X  X  X  X  X  X  X  X
 0 X^2  0  0 X^2  0 X^2 X^2 2X^2  0  0 X^2 X^2  0 2X^2 X^2 2X^2 2X^2  0 X^2 2X^2  0 X^2 2X^2 2X^2 2X^2 2X^2  0  0  0 X^2 X^2  0 X^2 X^2 2X^2  0  0 X^2 X^2  0 2X^2 X^2 2X^2 2X^2  0 X^2 2X^2  0 X^2 2X^2 2X^2 2X^2 2X^2  0  0 X^2 X^2  0 2X^2 X^2 X^2 X^2  0 X^2  0 X^2 2X^2 2X^2  0  0 2X^2 X^2  0 X^2 2X^2 2X^2 2X^2 2X^2  0
 0  0 X^2  0 2X^2 X^2 2X^2 X^2 2X^2  0 X^2 X^2  0 2X^2  0  0 X^2 X^2 2X^2 2X^2 2X^2 2X^2 X^2  0  0 X^2 2X^2  0  0 X^2 2X^2 X^2 X^2 2X^2  0 2X^2  0 X^2 X^2  0 2X^2  0  0 X^2 X^2 2X^2 2X^2 2X^2 2X^2 X^2  0  0 X^2 2X^2  0 X^2 2X^2 X^2 X^2  0 X^2  0 2X^2 X^2 X^2  0  0  0 X^2 2X^2 2X^2 X^2 2X^2 2X^2  0  0 X^2 2X^2 2X^2  0
 0  0  0 X^2 2X^2 2X^2  0 2X^2 2X^2 2X^2 X^2  0 2X^2  0 2X^2 X^2 X^2  0 X^2 X^2 X^2 2X^2 X^2  0 X^2 2X^2  0  0 X^2 2X^2 2X^2 2X^2 X^2 X^2 X^2 2X^2 2X^2  0  0  0 X^2 X^2 2X^2 2X^2 X^2  0  0  0 2X^2 X^2  0 2X^2  0 X^2 X^2 2X^2 2X^2 2X^2 X^2 X^2  0  0  0  0 X^2 2X^2 X^2  0 2X^2 2X^2 X^2  0 X^2  0 2X^2 2X^2 X^2  0 X^2  0

generates a code of length 80 over Z3[X]/(X^3) who´s minimum homogenous weight is 159.

Homogenous weight enumerator: w(x)=1x^0+156x^159+486x^160+80x^162+6x^186

The gray image is a linear code over GF(3) with n=720, k=6 and d=477.
This code was found by Heurico 1.16 in 0.201 seconds.