The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+1054x^54+1098x^55+2358x^56+5202x^57+9036x^58+9234x^59+20664x^60+22140x^61+21762x^62+34064x^63+23850x^64+12654x^65+8928x^66+3654x^67+648x^68+648x^69+152x^72

The gray image is a code over GF(3) with n=279, k=11 and d=162.
This code was found by Heurico 1.16 in 27.2 seconds.