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

generates a code of length 57 over Z27 who´s minimum homogenous weight is 111.

Homogenous weight enumerator: w(x)=1x^0+126x^111+162x^112+36x^114+324x^115+22x^117+54x^120+2x^135+2x^144

The gray image is a code over GF(3) with n=513, k=6 and d=333.
This code was found by Heurico 1.16 in 0.174 seconds.