The generator matrix

 1  0  1  1  1  1  1 21  1  1  1 24  0  1  1  1  1  1 21  1 24  1  1  1  0  1  1  1  1 21  1 24  1  1  1  1  1 24  1  1  1  1 21  1 24  1  1  1  1  1  1  1  1  0
 0  1  7 26 21  4 20  1 24 19 23  1  1  0 16 26 20  4  1 21  1 23 24 19  1  4 16 23 19  1 24  1  4 20 19 21 23  1 24  4 19  0  1 23  1  0 24  6  5 16 10 24 26  1
 0  0  9  0  0  0 18 18  9  9  9  0  9  0  9  0  9  9 18 18  9  9  0  9  0 18 18  9  0  0  0 18  9  0  0 18 18 18  9  0  0  9 18 18 18  0 18  0 18 18  0 18  9  0
 0  0  0  9  0  0 18 18 18  0  9  9 18  9 18  0 18  9 18  0 18  0 18 18  0  0 18  0 18  9 18  0  9  0  9 18 18  9  9 18 18  0  9 18  9  0  9 18 18  0  0  9  0  9
 0  0  0  0 18  0 18  9  9 18 18  9  0  0  0 18  0  0  9  9  9 18 18  9 18  0 18  0  0  0 18  0 18  9  9  0 18  9 18 18  9  0 18  0 18  9 18  0  0 18 18  0  9 18
 0  0  0  0  0  9 18  0 18 18 18 18 18 18  9  9 18  0 18  9 18  0  0  0  9  9  0  9  9  9  9  9  9  9  0 18  9 18  0 18  9  0  0  9 18  0 18 18  0  0  0  9  9  9

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

Homogenous weight enumerator: w(x)=1x^0+100x^96+60x^97+108x^98+496x^99+546x^100+546x^101+1754x^102+2514x^103+1680x^104+5324x^105+6468x^106+3150x^107+9384x^108+8664x^109+3156x^110+6876x^111+4602x^112+1392x^113+1180x^114+438x^115+144x^116+266x^117+24x^118+24x^119+48x^120+12x^121+6x^122+36x^123+28x^126+10x^129+2x^132+4x^135+6x^138

The gray image is a code over GF(3) with n=486, k=10 and d=288.
This code was found by Heurico 1.16 in 8.33 seconds.