The generator matrix

 1  0  1  1  1  1  1  1 18  1  1 21  1  1  1  1  1  1  3  1 21  1  1 24  1  1  1  1  1  1 15  0  1  1 15  1  1  1  1  1  1  9  0  1 24  1  1  1  1  1  1  1  1  1  1  1  1
 0  1  1 26 18 17  0 25  1 20  4  1 21 23 24  5 15  1  1 11  1 11 24  1 22 26 22 23 12  4  1  1 16 25  1 26 21 20 19 15  4  1  1  8  1 22  1 10 21 12  4 10  1 19 15 22 24
 0  0 24  9 21 12  6  3  3 18  0  6  0 18 15 24 12 21 12  3  0 15  9  6  3 24 18 12 12 24  3 15  6  9 18  0  6  6  9 18  6 12 18  3 15 21  6  0 21 24  9 24 12  3 24 15 21

generates a code of length 57 over Z27 who´s minimum homogenous weight is 109.

Homogenous weight enumerator: w(x)=1x^0+228x^109+720x^110+712x^111+918x^112+690x^113+690x^114+414x^115+564x^116+544x^117+480x^118+408x^119+60x^120+36x^121+42x^122+6x^123+12x^124+6x^125+6x^127+8x^129+12x^130+4x^135

The gray image is a code over GF(3) with n=513, k=8 and d=327.
This code was found by Heurico 1.16 in 0.154 seconds.