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  X  1  1
 0  X 2X  0 X+3 2X X+3 2X+6  0  6 X+3 2X  0 X+6 2X+3  6 X+6 2X  6 X+3  6 2X+6 X+6 2X+6  3 X+6 2X+6  0  0  6  6 X+3 X+3 X+6 X+6 2X 2X+6 2X+6 2X  0 X+3 2X  3  X 2X+3  6 2X+3  0  X X+3 2X+3  3 X+6 2X+3  3  X 2X+6  6 X+6 2X+3  X 2X+3  6  3  3  3 X+3 X+6 2X 2X+6  X 2X+3  0  3  X  X 2X+6 2X+3  3  X 2X  0 X+3 2X X+3  0  0
 0  0  6  0  3  3  6  0  6  3  3  0  6  0  6  6  0  6  3  6  0  3  6  0  3  3  3  0  6  6  0  3  6  6  3  0  3  0  3  3  0  6  6  6  6  0  0  3  0  0  6  3  3  3  6  6  6  3  0  0  3  3  6  0  0  3  0  6  0  6  3  3  3  0  3  6  6  0  6  0  3  0  3  0  3  6  0
 0  0  0  6  6  3  3  6  3  6  3  3  0  3  3  6  6  6  3  6  3  6  0  0  0  0  0  3  6  0  0  0  0  6  3  6  3  3  0  0  0  3  3  3  6  6  0  3  6  3  0  6  6  6  6  6  3  0  0  6  3  0  3  0  6  3  6  3  0  6  0  3  6  3  6  0  0  3  0  3  6  0  3  0  6  0  0

generates a code of length 87 over Z9[X]/(X^2+3,3X) who´s minimum homogenous weight is 168.

Homogenous weight enumerator: w(x)=1x^0+30x^168+52x^171+324x^172+1026x^174+648x^175+94x^177+10x^180+2x^258

The gray image is a code over GF(3) with n=783, k=7 and d=504.
This code was found by Heurico 1.16 in 0.401 seconds.