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

generates a code of length 87 over Z3[X]/(X^3) who´s minimum homogenous weight is 171.

Homogenous weight enumerator: w(x)=1x^0+318x^171+1674x^174+54x^177+134x^180+2x^189+4x^207

The gray image is a linear code over GF(3) with n=783, k=7 and d=513.
This code was found by Heurico 1.16 in 0.29 seconds.