The generator matrix

 1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  3  1  3  3  1  3  3  3  3  1  1  1
 0  9  0  0  0  0  0  0  0  0  0  0  0  9  9 18 18 18  9 18  9  9  9  9  9  0  0  9  9  9  9  0  9  9
 0  0  9  0  0  0  0  0  0  0  0  9  9 18  9  0  9 18 18 18  0  0 18  9  9  9  9  0 18 18  0 18  9 18
 0  0  0  9  0  0  0  0  9 18 18 18 18 18  9  0  9 18  0  0  0 18  0 18 18  0  0  9 18  9  9  0  9 18
 0  0  0  0  9  0  0  9 18  0 18 18  9  9  9 18  9  9  0 18  9 18 18 18  0 18 18  0 18 18 18  9 18  9
 0  0  0  0  0  9  0 18 18  9  0 18 18  9 18 18  9 18 18  9 18  9  0 18  0 18  0 18  0  0  0  0  0  0
 0  0  0  0  0  0  9 18 18 18 18  9  0  9  9  0  0  9 18  9  9  9 18  9 18 18  9  0  9  9  0 18 18 18

generates a code of length 34 over Z27 who´s minimum homogenous weight is 54.

Homogenous weight enumerator: w(x)=1x^0+140x^54+214x^57+396x^60+762x^63+1426x^66+13122x^68+1564x^69+1228x^72+466x^75+184x^78+106x^81+54x^84+16x^87+4x^90

The gray image is a code over GF(3) with n=306, k=9 and d=162.
This code was found by Heurico 1.16 in 1.68 seconds.