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  3  3  0  1  1  3  3  9  1  1  1  1  1  3  3 18  1  1  1  1  1  1  1  1  1  1  1  3  3  0  3  3  9  3  3 18  3  3  3  3  3  1  1
 0  3 24  9 21  6 18 12 15  0 21 24  9 12  6 18  3 15  0 21 24  9 12  6 18  3 15  0 21 24  9 12  6 18  3 15 21 24  3  0 21 12  6  3 24  9 12  6 18  3 15  3  3 15  0  9 18 21 12  3 24  6 15 21 24  3 12  6  3  3 15  3  0  9 18 21 12  0  9

generates a code of length 79 over Z27 who´s minimum homogenous weight is 157.

Homogenous weight enumerator: w(x)=1x^0+54x^157+144x^158+24x^160+12x^163+4x^168+4x^174

The gray image is a code over GF(3) with n=711, k=5 and d=471.
This code was found by Heurico 1.16 in 0.184 seconds.