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

generates a code of length 56 over Z9[X]/(X^2+3,3X) who´s minimum homogenous weight is 111.

Homogenous weight enumerator: w(x)=1x^0+42x^111+162x^112+26x^114+2x^117+6x^120+4x^123

The gray image is a code over GF(3) with n=504, k=5 and d=333.
This code was found by Heurico 1.16 in 0.0491 seconds.