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  1  1  1  2  1  2  1  1  2  1  1  4  2  2  1  2  1  1  1  2  1  1  2  0  2  1  2  0  1  4  1  0  2  1  1
 0 12  0  4  0  0  4 12  0  8  4  4  0 12 12  8  8 12  0  4  4  0  4  8  4  4  0  0  8  8 12 12  4 12 12  4  0  8  8  8  4  4 12  4  4  0  8 12 12  8  8  8 12  4 12  0  8
 0  0 12  4  0 12  4  0  8  4  0  4  0  4  8  4  4  0  0  4 12 12  8  8  0 12 12 12  4  8  8 12 12  0  8 12  8  4 12  8  0 12  4  4  4  4  4  0  0  4 12  4  0  8  0  0  0
 0  0  0  8  0  0  0  0  8  8  8  8  8  0  8  0  8  0  8  0  8  8  0  8  0  0  0  0  8  0  8  0  0  8  0  0  8  8  0  0  0  8  0  8  0  0  8  8  0  0  8  8  8  0  8  0  8
 0  0  0  0  8  0  0  0  0  0  0  8  8  8  0  0  0  0  0  8  8  8  8  0  8  8  8  8  0  8  0  8  0  0  8  8  0  8  0  0  8  8  0  0  8  8  0  0  8  8  0  8  8  8  8  8  0
 0  0  0  0  0  8  0  0  0  8  0  0  8  8  8  8  8  8  8  0  8  8  8  0  0  8  0  8  8  8  0  0  0  0  0  0  8  0  0  0  8  0  0  0  8  0  8  0  0  8  0  0  8  8  0  8  0
 0  0  0  0  0  0  8  0  8  8  8  8  8  0  8  8  0  8  0  8  8  0  8  8  0  0  0  8  0  0  0  0  8  0  0  0  0  8  8  8  0  8  0  0  0  8  0  0  8  0  0  0  8  8  8  8  8
 0  0  0  0  0  0  0  8  0  0  8  0  0  0  0  8  0  8  8  0  8  8  8  8  0  8  8  0  8  0  0  0  8  8  8  8  0  8  8  0  0  8  0  8  0  0  0  0  8  8  0  8  8  0  8  8  0

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

Homogenous weight enumerator: w(x)=1x^0+49x^48+50x^49+115x^50+128x^51+270x^52+150x^53+726x^54+640x^55+1428x^56+1164x^57+1440x^58+664x^59+698x^60+108x^61+208x^62+80x^63+86x^64+50x^65+50x^66+24x^67+24x^68+14x^69+16x^70+4x^72+2x^74+2x^78+1x^82

The gray image is a code over GF(2) with n=456, k=13 and d=192.
This code was found by Heurico 1.16 in 1.6 seconds.