The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+534x^55+696x^56+1804x^57+3840x^58+3102x^59+5676x^60+8400x^61+7212x^62+10154x^63+9336x^64+3672x^65+2498x^66+1614x^67+336x^68+28x^69+78x^70+42x^71+6x^72+12x^73+6x^74+2x^78

The gray image is a code over GF(3) with n=279, k=10 and d=165.
This code was found by Heurico 1.16 in 3.07 seconds.