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

generates a code of length 78 over Z27 who´s minimum homogenous weight is 154.

Homogenous weight enumerator: w(x)=1x^0+102x^154+522x^156+54x^157+36x^159+8x^162+6x^181

The gray image is a code over GF(3) with n=702, k=6 and d=462.
This code was found by Heurico 1.16 in 0.282 seconds.