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

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+10x^171+156x^173+516x^174+18x^177+16x^180+6x^183+6x^200

The gray image is a linear code over GF(3) with n=783, k=6 and d=513.
This code was found by Heurico 1.16 in 0.276 seconds.