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

generates a code of length 27 over Z27 who´s minimum homogenous weight is 54.

Homogenous weight enumerator: w(x)=1x^0+726x^54+2x^81

The gray image is a code over GF(3) with n=243, k=6 and d=162.
This code was found by Heurico 1.16 in 0.0059 seconds.