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

generates a code of length 54 over Z27 who´s minimum homogenous weight is 108.

Homogenous weight enumerator: w(x)=1x^0+56x^108+6x^110+6x^111+6x^113+6x^116

The gray image is a code over GF(3) with n=486, k=4 and d=324.
This code was found by Heurico 1.16 in 0.0428 seconds.