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

generates a code of length 56 over Z27 who´s minimum homogenous weight is 112.

Homogenous weight enumerator: w(x)=1x^0+54x^112+14x^114+8x^117+2x^120+2x^126

The gray image is a code over GF(3) with n=504, k=4 and d=336.
This code was found by Heurico 1.16 in 0.0491 seconds.