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

generates a code of length 56 over Z27 who´s minimum homogenous weight is 111.

Homogenous weight enumerator: w(x)=1x^0+42x^111+162x^112+26x^114+2x^117+6x^120+4x^123

The gray image is a code over GF(3) with n=504, k=5 and d=333.
This code was found by Heurico 1.16 in 0.0493 seconds.