The generator matrix

 1  0  1  1  1  1  1 21  1  1  1 24  1  1  1  9  1  1  1 12  1  1  1  6  1  1  1  1
 0  1 16 26 21  4 20  1 24 19 23  1  9  7  8  1 12 13 11  1  6 10  5  1 18  3 25 22

generates a code of length 28 over Z27 who´s minimum homogenous weight is 55.

Homogenous weight enumerator: w(x)=1x^0+312x^55+252x^56+156x^58+4x^60+4x^66

The gray image is a code over GF(3) with n=252, k=6 and d=165.
This code was found by Heurico 1.16 in 0.00325 seconds.