The generator matrix

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

generates a code of length 56 over Z16 who´s minimum homogenous weight is 46.

Homogenous weight enumerator: w(x)=1x^0+91x^46+32x^47+368x^48+188x^49+771x^50+832x^51+1300x^52+2688x^53+2896x^54+5456x^55+3528x^56+5496x^57+2749x^58+2736x^59+1640x^60+800x^61+544x^62+144x^63+279x^64+44x^65+93x^66+16x^67+36x^68+20x^70+16x^72+3x^74+1x^78

The gray image is a code over GF(2) with n=448, k=15 and d=184.
This code was found by Heurico 1.16 in 40 seconds.