The generator matrix

 1  0  1  1  1  1  1 18  1  1  1 21  0  1  1  1  1  3  1  1 24  1 15  1  1  1  1 24  1  1  1
 0  1  1 26 21 20 16  1 26 24  4  1  1 18 16 23 20  1 24  0  1  4  1 19 21  0 21  1  6 24 20
 0  0 24  0 18 18 15  3 24  0 15 15  6 21  9  6 24  3 24 15 15  9 12  0 15 18 15 15 12 24 18
 0  0  0  9  9  0 18  9  9 18  9  9  0  0 18  0 18  0  0 18 18  0 18  9  9 18  0  9  9  9  9

generates a code of length 31 over Z27 who´s minimum homogenous weight is 55.

Homogenous weight enumerator: w(x)=1x^0+102x^55+282x^56+444x^57+1296x^58+1242x^59+1348x^60+4020x^61+2166x^62+2168x^63+3996x^64+1548x^65+612x^66+180x^67+72x^68+38x^69+120x^70+30x^71+6x^73+6x^74+4x^75+2x^84

The gray image is a code over GF(3) with n=279, k=9 and d=165.
This code was found by Heurico 1.16 in 0.484 seconds.