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

generates a code of length 64 over Z9[X]/(X^2+3,3X) who´s minimum homogenous weight is 127.

Homogenous weight enumerator: w(x)=1x^0+24x^127+198x^128+12x^130+4x^132+2x^147+2x^165

The gray image is a code over GF(3) with n=576, k=5 and d=381.
This code was found by Heurico 1.16 in 0.0816 seconds.