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

generates a code of length 77 over Z27 who´s minimum homogenous weight is 153.

Homogenous weight enumerator: w(x)=1x^0+174x^153+486x^154+54x^156+8x^162+6x^180

The gray image is a code over GF(3) with n=693, k=6 and d=459.
This code was found by Heurico 1.16 in 0.304 seconds.