The generator matrix

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

generates a code of length 57 over Z16 who´s minimum homogenous weight is 47.

Homogenous weight enumerator: w(x)=1x^0+50x^47+124x^48+190x^49+322x^50+620x^51+777x^52+1742x^53+2152x^54+3968x^55+3790x^56+5360x^57+3889x^58+3920x^59+2144x^60+1712x^61+691x^62+602x^63+261x^64+194x^65+98x^66+52x^67+55x^68+18x^69+12x^70+4x^71+16x^72+3x^74+1x^78

The gray image is a code over GF(2) with n=456, k=15 and d=188.
This code was found by Heurico 1.16 in 18.7 seconds.