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
 0  3  0  3  0  3  6  6  6  0  0  3  3  0  3  6  6  6  0  0  3  3  0  3  6  6  6  0
 0  0  3  6  6  3  0  3  6  0  3  6  3  6  0  0  3  6  0  3  6  3  6  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+8x^54+54x^56+16x^57+2x^84

The gray image is a code over GF(3) with n=84, k=4 and d=54.
This code was found by Heurico 1.16 in 0.00221 seconds.