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

generates a code of length 57 over Z27 who´s minimum homogenous weight is 110.

Homogenous weight enumerator: w(x)=1x^0+162x^110+110x^111+216x^112+228x^113+708x^114+432x^115+174x^116+36x^117+54x^119+26x^120+24x^122+6x^123+6x^125+2x^126+2x^165

The gray image is a code over GF(3) with n=513, k=7 and d=330.
This code was found by Heurico 1.16 in 0.0797 seconds.