The generator matrix

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

generates a code of length 30 over Z27 who´s minimum homogenous weight is 56.

Homogenous weight enumerator: w(x)=1x^0+60x^56+24x^57+48x^59+514x^60+20x^63+48x^65+6x^66+6x^68+2x^78

The gray image is a code over GF(3) with n=270, k=6 and d=168.
This code was found by Heurico 1.16 in 0.403 seconds.