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

generates a code of length 84 over Z27 who´s minimum homogenous weight is 169.

Homogenous weight enumerator: w(x)=1x^0+54x^169+20x^171+2x^174+2x^177+2x^180

The gray image is a code over GF(3) with n=756, k=4 and d=507.
This code was found by Heurico 1.16 in 0.235 seconds.