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

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

Homogenous weight enumerator: w(x)=1x^0+786x^55+1128x^56+954x^57+3594x^58+2358x^59+1574x^60+3882x^61+2172x^62+938x^63+1752x^64+492x^65+12x^66+24x^67+4x^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 0.683 seconds.