The generator matrix

 1  0  1  1  1 12  1  1  2  1  6  1  1  1  1  8  1 10  1  1  1  8  1 14  4  1  1  1  6  1  1  1  1  1  2 10  1  2  6  1  0  1  0  1  4  1  2 12  1  1  0 14  1  1  1  1
 0  1  1 12 11  1  2  5  1  6  1  7  4 13  7  1  5  1 11 14  4  1 10  1  1  0  9 15  1  8  6  2  1  1  1  1 15  4  1 10  1  3  2  0  1  0  8  1 10 14  1  1  3  2  0  2
 0  0  2  6  4  6  2  0 10  0  8  2 10  4 12  4  6 14  2  4  4  2  6  4 10  6 14 14 14  2  6 12  2  4  4 14  8  2  8  8  8  8  6  6 12 14  2  0 12  8  4  0  6  2  6 10
 0  0  0  8  0  0  0  0  8  0  0  0  0  8  8  0  8  8  8  0  8  0  8  8  0  8  0  8  0  0  8  0  8  8  0  8  8  0  0  8  8  8  8  8  8  0  8  0  8  0  8  8  0  0  0  8
 0  0  0  0  8  0  0  0  0  8  8  0  0  8  0  8  8  8  0  8  0  8  0  8  0  8  0  8  0  8  8  0  8  0  8  0  8  0  8  8  0  8  0  0  0  0  8  0  8  8  8  8  0  0  8  0
 0  0  0  0  0  8  0  0  8  0  0  0  0  0  0  0  0  8  0  8  8  8  8  0  8  8  0  0  8  0  8  0  8  8  8  0  8  0  8  0  0  8  8  0  8  8  0  8  0  0  8  0  8  8  0  8
 0  0  0  0  0  0  8  0  8  0  0  0  8  8  8  8  8  8  8  0  8  8  0  0  8  0  8  0  8  0  8  8  0  0  8  8  8  8  8  0  8  0  8  8  8  0  8  8  0  8  0  8  0  8  8  8
 0  0  0  0  0  0  0  8  0  8  8  8  8  0  8  0  8  0  8  0  0  0  8  8  8  0  0  8  0  8  8  0  8  8  8  0  0  0  0  0  8  8  0  0  0  0  0  8  8  8  8  8  8  8  0  8

generates a code of length 56 over Z16 who´s minimum homogenous weight is 47.

Homogenous weight enumerator: w(x)=1x^0+50x^47+197x^48+382x^49+1006x^50+1440x^51+3079x^52+4676x^53+7207x^54+9264x^55+10776x^56+9462x^57+7335x^58+4658x^59+3127x^60+1394x^61+785x^62+308x^63+206x^64+84x^65+42x^66+22x^67+15x^68+2x^69+7x^70+2x^71+4x^72+1x^74+3x^76+1x^78

The gray image is a code over GF(2) with n=448, k=16 and d=188.
This code was found by Heurico 1.16 in 40.2 seconds.