The generator matrix

 1  0  1  1  1  1  1 21  1  1  1  0  1  1  1 24  1  1  1  1  1  1 21 24  1  1  1  1  1  1  1
 0  1  7 26  4 21 20  1  0 16 26  1 24 19 23  1  4 21 24 19 20 23  1  1  9 12  6 16 13 10  9
 0  0  9  0 18 18  9  9  9  0 18 18 18 18  9  9  9  9  0  0 18  0 18  0 18  0  9 18  0  9  9

generates a code of length 31 over Z27 who´s minimum homogenous weight is 58.

Homogenous weight enumerator: w(x)=1x^0+108x^58+294x^59+114x^60+432x^61+396x^62+86x^63+432x^64+270x^65+38x^66+12x^68+4x^75

The gray image is a code over GF(3) with n=279, k=7 and d=174.
This code was found by Heurico 1.16 in 0.0122 seconds.