The generator matrix

 1  0  1  1  1  1  1  0  1  1  1 15  1  1  1 24  1  3  1 12  1  1  1  1  1  1  1  1  1  6  1
 0  1  1 26 18 25 17  1  0 22 26  1  3 19 20  1  4  1  5  1 22  0 26 21 21 20 15 12 24  1 25
 0  0 24  0 18  0 21 24 18 21 15 12  3 24 18  0  9 21  0 15 15 15 12 15 18  6 24 12  9 15  9
 0  0  0  3 21 12 18  9 24  6 15  0 18 15 15  6 24 15  9  3  3  0  3  6  0 12 12 21 12 15 21

generates a code of length 31 over Z27 who´s minimum homogenous weight is 54.

Homogenous weight enumerator: w(x)=1x^0+506x^54+198x^55+612x^56+1782x^57+3258x^58+2628x^59+5544x^60+9126x^61+9018x^62+8742x^63+10062x^64+3708x^65+2298x^66+684x^67+72x^68+648x^69+156x^72+6x^75

The gray image is a code over GF(3) with n=279, k=10 and d=162.
This code was found by Heurico 1.16 in 7.49 seconds.