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

generates a code of length 51 over Z27 who´s minimum homogenous weight is 96.

Homogenous weight enumerator: w(x)=1x^0+534x^96+800x^99+972x^100+648x^101+660x^102+972x^103+1296x^104+228x^105+178x^108+144x^111+102x^114+18x^117+6x^120+2x^144

The gray image is a code over GF(3) with n=459, k=8 and d=288.
This code was found by Heurico 1.16 in 20 seconds.