The generator matrix

 1  0  1  1  1  1  1  0  1  1  1  3  1  1  1  3  1  1  1  1  1  1  0  3  1  1  3  1
 0  1  1  8  7  0  8  1  3  7  2  1  3  4  2  1  4  1  0  3  8  2  1  1  6  6  0  6
 0  0  6  0  3  3  6  6  6  0  3  3  3  6  6  6  3  0  6  0  3  0  3  0  0  3  6  0

generates a code of length 28 over Z9 who´s minimum homogenous weight is 54.

Homogenous weight enumerator: w(x)=1x^0+128x^54+72x^57+18x^60+24x^63

The gray image is a code over GF(3) with n=84, k=5 and d=54.
This code was found by Heurico 1.16 in 0.00291 seconds.