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

generates a code of length 57 over Z16 who´s minimum homogenous weight is 55.

Homogenous weight enumerator: w(x)=1x^0+132x^55+209x^56+404x^57+152x^58+76x^59+21x^60+28x^61+1x^108

The gray image is a code over GF(2) with n=456, k=10 and d=220.
This code was found by Heurico 1.16 in 9.4 seconds.