The generator matrix

 1  0  1  1  1  1  1 18  1 24  1  1  1  1  0  1  1  1  6  1  1  1  1  1 21  1  1  1  1  1
 0  1  1 26  0 25 17  1 18  1 25  2  9 16  1 14 25  3  1 12 24 13  6 26  1  9  2  0  6  0
 0  0 24  0  9  3 21  3 21  6 12 21  3  6 21 24  6  9  9 12 15  0 15 18 15 21 21 24  9  9
 0  0  0  3 15  9 15 15  9  0  6 18  6  6 12 21 21 21  3 18 24  6 18  9  6 21  9 18 12  9

generates a code of length 30 over Z27 who´s minimum homogenous weight is 51.

Homogenous weight enumerator: w(x)=1x^0+108x^51+180x^52+324x^53+1190x^54+1224x^55+2388x^56+3796x^57+5520x^58+6654x^59+12010x^60+10068x^61+7500x^62+4600x^63+1764x^64+528x^65+776x^66+168x^67+96x^68+104x^69+30x^70+6x^71+14x^72

The gray image is a code over GF(3) with n=270, k=10 and d=153.
This code was found by Heurico 1.16 in 3.73 seconds.