The generator matrix

 1  0  1  1  1  1  1 21  1  1  1 24  1  1  1  9  1  1  1 12  1  1  1  6  1  1  1 18  1  1  1  3  1  1  1 15  1  1  1  0  1  1  1 21  1  1  1 24  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  9 12  6 18  3 15  1
 0  1 16 26 21  4 20  1 24 19 23  1  9  7  8  1 12 13 11  1  6 10  5  1 18 25 17  1  3 22  2  1 15  1 14  1  0 16 26  1 21  4 20  1 24 19 23  1  9 12  7 13  6 10  8 11  5 18  3 15 25 22  1 17  2 14  1  1  1  1  1  1  0

generates a code of length 73 over Z27 who´s minimum homogenous weight is 144.

Homogenous weight enumerator: w(x)=1x^0+24x^144+648x^146+48x^147+2x^162+6x^165

The gray image is a code over GF(3) with n=657, k=6 and d=432.
This code was found by Heurico 1.16 in 0.0916 seconds.