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

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

Homogenous weight enumerator: w(x)=1x^0+48x^157+162x^158+16x^159+8x^162+6x^175+2x^186

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 0.185 seconds.