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

generates a code of length 57 over Z16 who´s minimum homogenous weight is 54.

Homogenous weight enumerator: w(x)=1x^0+36x^54+350x^56+256x^57+344x^58+32x^60+4x^62+1x^112

The gray image is a code over GF(2) with n=456, k=10 and d=216.
This code was found by Heurico 1.16 in 0.199 seconds.