The generator matrix

 1  0  1  1  1  1  1  1 18  1 21  1  1  0  1  1  1  1  1  1  6  1  1  1  1  6  1 24 12  1
 0  1  1 26 18 17  0 25  1 20  1 21 20  1 22 24  2 13 23 21  1 26  6 24 23  1  5  1  1 16
 0  0 24  9 21 12  6  3  3 18  0  0 15  6 21  9  3 18  6 24 24  6 21 24  3 21 18 18  6  9

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

Homogenous weight enumerator: w(x)=1x^0+78x^55+228x^56+1246x^57+378x^58+690x^59+1308x^60+588x^61+654x^62+1244x^63+54x^64+30x^65+6x^66+6x^67+18x^68+30x^70+2x^75

The gray image is a code over GF(3) with n=270, k=8 and d=165.
This code was found by Heurico 1.16 in 0.0543 seconds.