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  X  1  1  1  1  X  1  1  1  X  X  1  1  1  X  1  1  1  X  1
 0 X^2  0  0  0  0  0  0  0  0  0  0  0  0 X^2 2X^2 2X^2 X^2 2X^2 2X^2 2X^2  0 X^2 X^2 X^2 2X^2 X^2  0 2X^2 2X^2 X^2 2X^2 X^2 X^2 X^2 X^2 X^2 2X^2 X^2 X^2 X^2 X^2  0 X^2  0  0 X^2 X^2 X^2 X^2  0 2X^2  0 2X^2  0 X^2
 0  0 X^2  0  0  0  0  0  0  0  0 X^2 2X^2 2X^2 2X^2 2X^2  0 X^2 X^2 2X^2 X^2 2X^2  0 X^2 X^2  0 X^2 X^2 X^2 X^2  0 X^2  0 2X^2  0  0  0 X^2 X^2 X^2  0 2X^2 2X^2  0 2X^2 X^2  0 X^2  0 2X^2  0 2X^2 2X^2  0 X^2 X^2
 0  0  0 X^2  0  0  0  0 X^2 2X^2 2X^2 2X^2  0  0 X^2  0 X^2 2X^2 2X^2  0 X^2  0 2X^2 X^2  0  0 X^2 2X^2 2X^2  0  0 X^2 2X^2  0 2X^2 2X^2 X^2 2X^2  0 2X^2 2X^2 X^2 X^2 X^2  0 2X^2 X^2 2X^2 2X^2  0 X^2 X^2 X^2  0 X^2 2X^2
 0  0  0  0 X^2  0  0 X^2 2X^2  0 2X^2  0  0 2X^2 2X^2 X^2 X^2 X^2  0 2X^2 2X^2 2X^2 X^2 2X^2 X^2 X^2 X^2 2X^2 X^2  0  0  0  0 X^2 X^2  0 2X^2  0 2X^2  0  0 X^2 X^2 X^2 2X^2  0 X^2 X^2 X^2  0 2X^2 X^2 2X^2 X^2 X^2 X^2
 0  0  0  0  0 X^2  0 2X^2 2X^2 X^2  0 2X^2 2X^2 2X^2 2X^2 2X^2 2X^2  0  0  0 2X^2 X^2  0 X^2  0 2X^2 X^2 X^2  0  0 2X^2  0  0 X^2 X^2 X^2 2X^2 2X^2 2X^2 X^2  0 2X^2 X^2  0 X^2 2X^2 X^2 2X^2  0  0 X^2  0 X^2  0 X^2  0
 0  0  0  0  0  0 X^2 2X^2 2X^2 2X^2 2X^2 2X^2 2X^2 X^2 X^2 X^2  0 2X^2 X^2 2X^2 2X^2 2X^2 X^2  0 2X^2 2X^2 X^2 2X^2  0  0 X^2 X^2 X^2 X^2 2X^2 X^2 X^2 X^2  0 2X^2  0 2X^2  0 X^2  0 X^2  0 2X^2  0 X^2  0  0  0 2X^2 2X^2 X^2

generates a code of length 56 over Z3[X]/(X^3) who´s minimum homogenous weight is 96.

Homogenous weight enumerator: w(x)=1x^0+132x^96+184x^99+6x^100+246x^102+72x^103+216x^105+360x^106+208x^108+960x^109+170x^111+14562x^112+204x^114+1152x^115+194x^117+384x^118+204x^120+146x^123+112x^126+72x^129+52x^132+30x^135+10x^138+4x^141+2x^150

The gray image is a linear code over GF(3) with n=504, k=9 and d=288.
This code was found by Heurico 1.16 in 2.88 seconds.