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  3  1  1  1  1  1  3  1  1  0  1  1  3  1  1  9  1
 0  3 24  0 21 24  0 21 24  9 21 24  6  0 21 12  6  9 24  0 21 12  3 24 15  0 24 12 15 21  9 18 12  9  9 12 18 21  9  6 18 12 15 24 24  3  3 12  0 21 21 18  9  3
 0  0  9  0  0  0  0 18  9  0  9 18 18  0  0  9  0  0  9 18 18  9  9  9 18  9  9  9  0  9  0 18  0 18  9  9 18 18  9  9  0  0  9 18  9  9  0  0 18  0  0  9 18  0
 0  0  0  9  0  0  0  0  0 18  0  9 18  9  9  9  9 18  9 18  9  9  0 18 18  9  0  0 18  9  0  0  9  0  9 18  9  0 18  0  9 18  9 18  9  0  0  0  9 18  0 18  0  9
 0  0  0  0 18  0  9 18  9  9  0  9 18  0 18  0 18  0 18 18  0  0  0  0  9 18 18 18  0 18 18 18 18 18  0  0  9  0 18  0  9  9  9 18 18  9 18  9 18 18  0  0 18  9
 0  0  0  0  0  9  9  0 18  9  0  0  9  9 18 18  9  9  0 18  0  0  9 18  0  9  0  9  9  9 18 18  0  9 18 18  0  9  9  9  0  0  0 18 18  9  9  9 18 18  9  0  0 18

generates a code of length 54 over Z27 who´s minimum homogenous weight is 96.

Homogenous weight enumerator: w(x)=1x^0+176x^96+84x^97+6x^98+344x^99+162x^100+60x^101+590x^102+222x^103+1212x^104+1568x^105+204x^106+4368x^107+2542x^108+282x^109+4368x^110+1868x^111+216x^112+192x^113+518x^114+144x^115+242x^117+96x^118+72x^120+48x^121+48x^123+24x^126+6x^129+12x^132+6x^135+2x^147

The gray image is a code over GF(3) with n=486, k=9 and d=288.
This code was found by Heurico 1.16 in 1.9 seconds.