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

generates a code of length 78 over Z27 who´s minimum homogenous weight is 153.

Homogenous weight enumerator: w(x)=1x^0+70x^153+72x^154+108x^155+1728x^156+72x^157+54x^158+54x^159+18x^160+8x^162+2x^234

The gray image is a code over GF(3) with n=702, k=7 and d=459.
This code was found by Heurico 1.16 in 0.209 seconds.