The generator matrix

 1  0  0  0  1  1  1 18  1  1  1  1  1  1  1 15  1 21  1 24 18  1  1  1  1  3  1  1  1  1  1
 0  1  0  0 18  1 19  1  3 21 14 23  2 17 25  1 22  1 11  1 21 14  7 16  1  1  0  3 26  1 15
 0  0  1  0 16 25 14  7  4 20 12 19 26 18 21 14 12  8 10 24  1  0 24 11 26 20 12  8 15  4 25
 0  0  0  1 14  9  5  5  1 21  4 12 17 11  0 21 19 17 11 10 23  6  8 19 24 10 20  9  3 13  0

generates a code of length 31 over Z27 who´s minimum homogenous weight is 53.

Homogenous weight enumerator: w(x)=1x^0+774x^53+1408x^54+4728x^55+9300x^56+12014x^57+25470x^58+36294x^59+48612x^60+71136x^61+82860x^62+78368x^63+73590x^64+48954x^65+21698x^66+11592x^67+3954x^68+402x^69+72x^70+102x^71+62x^72+36x^73+12x^74+2x^75

The gray image is a code over GF(3) with n=279, k=12 and d=159.
This code was found by Heurico 1.16 in 215 seconds.