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  3  1  1  1  1  3  1  1  1  3  3  1  1  1  3  1  1  1  3  1
 0  9  0  0  0  0  0  0  0  0  0  0  0  0  9 18 18  9 18 18 18  0  9  9  9 18  9  0 18 18  9 18  9  9  9  9  9 18  9  9  9  9  0  9  0  0  9  9  9  9  0 18  0 18  0  9
 0  0  9  0  0  0  0  0  0  0  0  9 18 18 18 18  0  9  9 18  9 18  0  9  9  0  9  9  9  9  0  9  0 18  0  0  0  9  9  9  0 18 18  0 18  9  0  9  0 18  0 18 18  0  9  9
 0  0  0  9  0  0  0  0  9 18 18 18  0  0  9  0  9 18 18  0  9  0 18  9  0  0  9 18 18  0  0  9 18  0 18 18  9 18  0 18 18  9  9  9  0 18  9 18 18  0  9  9  9  0  9 18
 0  0  0  0  9  0  0  9 18  0 18  0  0 18 18  9  9  9  0 18 18 18  9 18  9  9  9 18  9  0  0  0  0  9  9  0 18  0 18  0  0  9  9  9 18  0  9  9  9  0 18  9 18  9  9  9
 0  0  0  0  0  9  0 18 18  9  0 18 18 18 18 18 18  0  0  0 18  9  0  9  0 18  9  9  0  0 18  0  0  9  9  9 18 18 18  9  0 18  9  0  9 18  9 18  0  0  9  0  9  0  9  0
 0  0  0  0  0  0  9 18 18 18 18 18 18  9  9  9  0 18  9 18 18 18  9  0 18 18  9 18  0  0  9  9  9  9 18  9  9  9  0 18  0 18  0  9  0  9  0 18  0  9  0  0  0 18 18  9

generates a code of length 56 over Z27 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 code over GF(3) with n=504, k=9 and d=288.
This code was found by Heurico 1.16 in 2.85 seconds.