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

generates a code of length 39 over Z27 who´s minimum homogenous weight is 78.

Homogenous weight enumerator: w(x)=1x^0+234x^78+2x^81+6x^90

The gray image is a code over GF(3) with n=351, k=5 and d=234.
This code was found by Heurico 1.16 in 0.0128 seconds.