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

generates a code of length 87 over Z27 who´s minimum homogenous weight is 174.

Homogenous weight enumerator: w(x)=1x^0+222x^174+6x^180+12x^183+2x^189

The gray image is a code over GF(3) with n=783, k=5 and d=522.
This code was found by Heurico 1.16 in 1.08 seconds.