The generator matrix

 1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  3  3  0  3  3  9  1  1  3  3
 0  3 24  9 21  6 18 12 15  0 21 24  9 12  6 18  3 15 21 24  3 12  6  3  0  9  3 15

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

Homogenous weight enumerator: w(x)=1x^0+60x^55+144x^56+30x^58+4x^60+4x^66

The gray image is a code over GF(3) with n=252, k=5 and d=165.
This code was found by Heurico 1.16 in 0.00394 seconds.