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

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

Homogenous weight enumerator: w(x)=1x^0+46x^108+60x^110+128x^111+216x^112+36x^113+1076x^114+432x^115+36x^116+44x^117+12x^119+64x^120+18x^122+14x^123+2x^126+2x^168

The gray image is a code over GF(3) with n=513, k=7 and d=324.
This code was found by Heurico 1.16 in 0.0963 seconds.