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  X  X  X  X  X  X  X  X  1  1  1  1  1  1  1  1  1  X  X  X  X  X  X  X  X  6  6  6  6  6  0  1  X  1  1  6  0  0  X  1  1  1
 0  6  0  6  0  6  3  3  3  0  0  6  6  0  6  3  3  3  0  0  6  6  0  6  3  3  3  0  0  6  6  0  6  3  3  3  0  0  6  6  0  6  3  3  3  0  6  6  6  0  3  3  3  0  0  6  6  0  6  3  3  3  0  6  6  6  0  3  3  3  0  6  3  0  6  6  0  0  6  3  3  6  0  0  0  6  3
 0  0  6  3  3  6  0  6  3  0  6  3  6  3  0  0  6  3  0  6  3  6  3  0  0  6  3  0  6  3  6  3  0  0  6  3  0  6  3  6  3  0  0  6  3  6  3  6  0  3  0  6  3  0  6  3  6  3  0  0  6  3  6  3  6  0  3  0  6  3  6  3  0  3  0  3  0  0  6  3  6  0  6  0  6  3  0

generates a code of length 87 over Z9[X]/(X^2+3,3X) who�s minimum homogenous weight is 174.

Homogenous weight enumerator: w(x)=1x^0+222x^174+6x^180+12x^183+2x^189

The gray image is a code over GF(3) with n=783, k=5 and d=522.
This code was found by Heurico 1.16 in 1.07 seconds.