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

generates a code of length 87 over Z3[X]/(X^3) who´s minimum homogenous weight is 175.

Homogenous weight enumerator: w(x)=1x^0+54x^175+20x^177+2x^180+2x^183+2x^189

The gray image is a linear code over GF(3) with n=783, k=4 and d=525.
This code was found by Heurico 1.16 in 0.268 seconds.