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

generates a code of length 57 over Z16 who´s minimum homogenous weight is 48.

Homogenous weight enumerator: w(x)=1x^0+25x^48+212x^49+321x^50+680x^51+836x^52+1722x^53+2153x^54+3700x^55+4380x^56+4854x^57+4350x^58+3768x^59+2162x^60+1564x^61+792x^62+612x^63+239x^64+204x^65+48x^66+72x^67+34x^68+18x^69+15x^70+2x^72+2x^73+1x^80+1x^82

The gray image is a code over GF(2) with n=456, k=15 and d=192.
This code was found by Heurico 1.16 in 16.6 seconds.