The generator matrix

 1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  2  0  2 12  1  2  8  1  2  4  1  1  1  1  1  1  2  2  2  2  2  0  2 12  2  2  8  4  1  1  1  1  4  4  0  8  1  1
 0  2 12  6  8 14  4 10  0  6 12 10  8 14  4  2  6  2 10  2  0 14  2 12  2  2  8  4  6 10 14  2  0 12  8  4  6  2 10  2 14  2  2  2  0  8 12  4 12  4  4  4  0  8

generates a code of length 54 over Z16 who´s minimum homogenous weight is 54.

Homogenous weight enumerator: w(x)=1x^0+116x^54+3x^56+4x^58+3x^60+1x^68

The gray image is a code over GF(2) with n=432, k=7 and d=216.
This code was found by Heurico 1.16 in 0.0849 seconds.