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

generates a code of length 57 over Z27 who´s minimum homogenous weight is 108.

Homogenous weight enumerator: w(x)=1x^0+190x^108+60x^111+1638x^114+210x^117+66x^120+10x^126+10x^135+2x^153

The gray image is a code over GF(3) with n=513, k=7 and d=324.
This code was found by Heurico 1.16 in 0.213 seconds.