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

generates a code of length 56 over Z27 who´s minimum homogenous weight is 109.

Homogenous weight enumerator: w(x)=1x^0+96x^109+240x^110+8x^111+78x^112+108x^113+8x^114+96x^115+72x^116+2x^117+12x^119+4x^120+2x^123+2x^132

The gray image is a code over GF(3) with n=504, k=6 and d=327.
This code was found by Heurico 1.16 in 0.0694 seconds.