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

generates a code of length 56 over Z27 who´s minimum homogenous weight is 102.

Homogenous weight enumerator: w(x)=1x^0+160x^102+144x^103+240x^104+596x^105+354x^106+492x^107+1362x^108+660x^109+1608x^110+3186x^111+2088x^112+2562x^113+3058x^114+774x^115+666x^116+558x^117+150x^118+132x^119+246x^120+120x^121+96x^122+252x^123+60x^124+30x^125+50x^126+18x^127+6x^128+6x^129+6x^130+2x^147

The gray image is a code over GF(3) with n=504, k=9 and d=306.
This code was found by Heurico 1.16 in 1.65 seconds.