The generator matrix

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

generates a code of length 81 over Z3[X]/(X^3) who´s minimum homogenous weight is 159.

Homogenous weight enumerator: w(x)=1x^0+342x^159+54x^160+108x^161+1334x^162+108x^163+54x^164+18x^165+162x^168+6x^189

The gray image is a linear code over GF(3) with n=729, k=7 and d=477.
This code was found by Heurico 1.16 in 0.223 seconds.