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  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  3  3  3  3  3  1  1  3  3  3  1  1  1  1  1  1  1  1  1  1  3  3  3  3  3  3  3  3  3  1  1  1  1  1  1  1
 0  9  0  9  0  9 18 18 18  0  0  9  9  0  9 18 18 18  0  0  9  9  0  9 18 18 18  0  0  9  9  0  9 18 18 18  0  0  9  9  0  9  9  9 18  0 18 18 18  0  9 18 18  0  0  9  9  0  9 18 18 18  0  9  9  0  9 18 18 18  0  0  0  9  9  0  9 18
 0  0  9 18 18  9  0  9 18  0  9 18  9 18  0  0  9 18  0  9 18  9 18  0  0  9 18  0  9 18  9 18  0  0  9 18  0  9 18  9 18  0 18  9  0  9 18  0  9 18  0  9 18  0  9 18  9 18  0  0  9 18  9 18  9 18  0  0  9 18  0  0  9 18  9 18  0  0

generates a code of length 78 over Z27 who´s minimum homogenous weight is 155.

Homogenous weight enumerator: w(x)=1x^0+48x^155+172x^156+12x^159+2x^162+6x^173+2x^183

The gray image is a code over GF(3) with n=702, k=5 and d=465.
This code was found by Heurico 1.16 in 0.176 seconds.