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

generates a code of length 57 over Z27 who´s minimum homogenous weight is 111.

Homogenous weight enumerator: w(x)=1x^0+180x^111+360x^114+184x^117+2x^135+2x^144

The gray image is a code over GF(3) with n=513, k=6 and d=333.
This code was found by Heurico 1.16 in 0.0734 seconds.