The generator matrix

 1  0  0  1  1  1  1  1  1  1  1 24  9  1  1  6 12  3  1  1  1  1 21  1  1  1  0  1  1  1
 0  1  0 18 21 16 25 20 22 23 17  1  1  3 11  1 24  1  4  5 26 12  1  7  0 23  6  7 19  6
 0  0  1 16 14  5 25  9 21  4 20  4  8 12  4  6  1 10 25  8 24 22  5 11 17 10  1 19  1 17

generates a code of length 30 over Z27 who´s minimum homogenous weight is 55.

Homogenous weight enumerator: w(x)=1x^0+726x^55+1158x^56+1534x^57+2574x^58+2340x^59+2708x^60+3078x^61+2124x^62+1478x^63+1368x^64+522x^65+14x^66+24x^67+6x^68+16x^69+6x^70+6x^71

The gray image is a code over GF(3) with n=270, k=9 and d=165.
This code was found by Heurico 1.16 in 0.46 seconds.