The generator matrix

 1  0  1  1  1  1  1  1 21  1  1 24  1  1 21 12  1  1  0  9  1  1  1  6  1 18  3  3  1  1
 0  1  1 26 18 17  0 25  1 13 20  1  3  6  1  1 21 21  1  1 15  3  1  1  3  1 24  1 22 14
 0  0 24  9 21 12  6  3  0 18 15  9 21  6 24  3  0 15  6 12 18 24 21  6 12  3  6 12  3  3

generates a code of length 30 over Z27 who´s minimum homogenous weight is 56.

Homogenous weight enumerator: w(x)=1x^0+618x^56+624x^57+774x^58+912x^59+798x^60+828x^61+972x^62+576x^63+180x^64+210x^65+16x^66+24x^68+6x^69+18x^71+2x^72+2x^75

The gray image is a code over GF(3) with n=270, k=8 and d=168.
This code was found by Heurico 1.16 in 43.2 seconds.