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  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
 0  X  0  3 2X X+6  X 2X+6 2X  3 X+6 2X+6  6  6 2X 2X+6 X+6  X 2X+3 2X+3  6  6 2X+3  X X+6  0 X+3 X+3  3 2X+6 2X  0 X+6  3 2X+3 X+3 X+3 X+3  3  6 X+6  0 2X 2X+3 2X 2X+6  X  0  3  X  6 X+3 2X+3 2X+6 2X+6 2X+3  0  X  0 2X 2X+6 X+3  3 X+3 2X  3  X  0 2X+3 X+3  3  X  6  6 X+6 X+6  6 X+6 2X+6 2X 2X+3  0  6 X+6  X  3
 0  0  X 2X+6  3 2X+6  X X+6 2X+3  3 X+6 2X  X 2X+3 2X+6  6 2X  6 X+6 2X X+6 2X+6  6 2X  6  3  X 2X+6  0 X+3  0 X+3  0 2X  X X+6  6 2X+3 X+6  0 X+3 2X+3  X 2X+3 X+3 2X+6 X+3 2X X+3 2X+3  3  0  3  3  X X+3  6 2X+6 2X+6 2X 2X+3 X+3  X  3  6 2X+3  3 X+6  0 2X  6 X+6  6 X+3  3 2X+3 2X  X  0 X+6 2X+6  0 X+6 2X+6  X  0

generates a code of length 86 over Z9[X]/(X^2+6,3X) who´s minimum homogenous weight is 168.

Homogenous weight enumerator: w(x)=1x^0+42x^168+36x^169+54x^170+80x^171+1710x^172+108x^173+114x^174+36x^175+4x^177+2x^258

The gray image is a code over GF(3) with n=774, k=7 and d=504.
This code was found by Heurico 1.16 in 0.293 seconds.