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

generates a code of length 85 over Z3[X]/(X^3) who´s minimum homogenous weight is 168.

Homogenous weight enumerator: w(x)=1x^0+20x^168+156x^169+486x^170+20x^171+30x^174+10x^177+6x^196

The gray image is a linear code over GF(3) with n=765, k=6 and d=504.
This code was found by Heurico 1.16 in 1.6 seconds.