The generator matrix

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

generates a code of length 29 over Z27 who´s minimum homogenous weight is 55.

Homogenous weight enumerator: w(x)=1x^0+30x^55+144x^56+12x^57+210x^58+288x^59+10x^60+30x^61+2x^63+2x^78

The gray image is a code over GF(3) with n=261, k=6 and d=165.
This code was found by Heurico 1.16 in 0.0148 seconds.