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  1  1  1  1  1  1 18  3 15  1  1  1  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  3 22 15  1 17  2 14  1  1  1  0 21 24  9

generates a code of length 40 over Z27 who´s minimum homogenous weight is 78.

Homogenous weight enumerator: w(x)=1x^0+42x^78+36x^79+540x^80+86x^81+18x^82+6x^93

The gray image is a code over GF(3) with n=360, k=6 and d=234.
This code was found by Heurico 1.16 in 0.0102 seconds.