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  3  3  3  3  3  1  3  3  3  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1
 0  9  0  9  0  9 18 18 18  0  0  9  9  0  9 18 18 18  0  0  9  9  0  9 18 18 18  0  0  9  9  0  9  9 18  0 18  9  9 18  0 18 18 18  0  0  9  9  0  9 18 18 18  0  0  9  9
 0  0  9 18 18  9  0  9 18  0  9 18  9 18  0  0  9 18  0  9 18  9 18  0  0  9 18  0  9 18  9 18 18  9  0  9 18  0  0  9 18  0  9 18  0  9 18  9 18  0  0  9 18  0  9 18  9

generates a code of length 57 over Z27 who´s minimum homogenous weight is 113.

Homogenous weight enumerator: w(x)=1x^0+48x^113+174x^114+8x^117+4x^120+6x^122+2x^147

The gray image is a code over GF(3) with n=513, k=5 and d=339.
This code was found by Heurico 1.16 in 0.0525 seconds.