The generator matrix

 1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  3  1  1  3  0  1  3  1  1  1  1  1
 0  3  0  0 24 21 15  3 24  9 24 21 21  9  0 24  6 12 12  9  0 15 21  3  9 24 21  6 21 24  9
 0  0  3 24  0 15 21  3  6 18  6  6 18 12  6 18  3 21  0  3  3 18  9  9  0  6 12 18  0  6 15
 0  0  0  9  0  0 18  0  0  9 18  9 18 18 18  0 18 18  9  0  9  9  9 18 18 18 18 18  9  9  0
 0  0  0  0  9 18  0  9 18  0 18 18  0  0  0 18 18  0 18 18 18  0 18  9  9  9 18  0  0 18  9

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

Homogenous weight enumerator: w(x)=1x^0+544x^54+54x^56+980x^57+324x^58+324x^59+3886x^60+1296x^61+2106x^62+6432x^63+1296x^64+432x^65+1304x^66+574x^69+102x^72+20x^75+4x^78+4x^81

The gray image is a code over GF(3) with n=279, k=9 and d=162.
This code was found by Heurico 1.16 in 7.74 seconds.