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

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

Homogenous weight enumerator: w(x)=1x^0+123x^48+430x^49+841x^50+1376x^51+1921x^52+3684x^53+4798x^54+6734x^55+8238x^56+9230x^57+8054x^58+7132x^59+4943x^60+3530x^61+2018x^62+1144x^63+566x^64+380x^65+181x^66+116x^67+40x^68+26x^69+12x^70+10x^71+7x^72+1x^80

The gray image is a code over GF(2) with n=456, k=16 and d=192.
This code was found by Heurico 1.16 in 59.5 seconds.