The generator matrix

 1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  3  3  1  1  1  3  3  1  3  1  1  3  3  3  3  1  1  1
 0  9 18  0  9 18  0  9 18  0  9 18  0  9 18  0  9 18  0  9 18  9 18  0  9 18  9 18  0  0  9 18  0  9 18  0  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+72x^78+6x^87+2x^90

The gray image is a code over GF(3) with n=351, k=4 and d=234.
This code was found by Heurico 1.16 in 0.0127 seconds.