The generator matrix

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

generates a code of length 48 over Z16 who´s minimum homogenous weight is 40.

Homogenous weight enumerator: w(x)=1x^0+183x^40+128x^41+686x^42+736x^43+2157x^44+1728x^45+4264x^46+3504x^47+5859x^48+3600x^49+4540x^50+1792x^51+1934x^52+672x^53+568x^54+112x^55+201x^56+16x^57+54x^58+29x^60+4x^64

The gray image is a code over GF(2) with n=384, k=15 and d=160.
This code was found by Heurico 1.16 in 13.1 seconds.