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

generates a code of length 78 over Z27 who´s minimum homogenous weight is 157.

Homogenous weight enumerator: w(x)=1x^0+66x^157+2x^159+6x^160+4x^165+2x^168

The gray image is a code over GF(3) with n=702, k=4 and d=471.
This code was found by Heurico 1.16 in 0.177 seconds.