The generator matrix

 1  0  0  1  1  1 21  1  1  1  1  1  1 24  1 18  1 18  1  1  6  1  1  1  1  1  1  1  3  1
 0  1  0 15  1 16  1  0 14 17 26 24  7  1 20  1  4  1 24 16  1 19 19 17 18  7  2 19 15 16
 0  0  1 25  1 15 14 26 19 20  0  9 23 23  6 21  6 19 14 22 19  8 23 16 25 12  8 24  1  4
 0  0  0 18 18 18  0  9  0  9 18  9 18 18  0 18  9  9  0  9  0  0  9 18  9  0 18  9  9  0

generates a code of length 30 over Z27 who´s minimum homogenous weight is 53.

Homogenous weight enumerator: w(x)=1x^0+252x^53+756x^54+2286x^55+3030x^56+3392x^57+6660x^58+7032x^59+8082x^60+11010x^61+7452x^62+4202x^63+3294x^64+1164x^65+286x^66+72x^67+24x^68+42x^69+6x^70+6x^72

The gray image is a code over GF(3) with n=270, k=10 and d=159.
This code was found by Heurico 1.16 in 2.99 seconds.