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

generates a code of length 57 over Z27 who´s minimum homogenous weight is 108.

Homogenous weight enumerator: w(x)=1x^0+596x^108+72x^109+108x^110+702x^111+756x^112+432x^113+846x^114+1512x^115+432x^116+576x^117+90x^118+150x^120+144x^123+112x^126+30x^129+2x^153

The gray image is a code over GF(3) with n=513, k=8 and d=324.
This code was found by Heurico 1.16 in 5.3 seconds.