The generator matrix

 1  0  1  1  1  4  1  1 14  1 10  1  8  1  1  1  6  1  1  6  1  1  1  1  1  2  1  1  1  2  1  4  1  1  0  2  1  1  2  0  1 12 10  2  1 14  1  1
 0  1  1  4  3  1  2  7  1 13  1  6  1  5 12 11  1 12  6  1  0 15 14  2 15  1  0 14 11  1  9  1 13 11  0 14  4  4  2  1 10  2  1 10  3  1  6 12
 0  0  2  2  0  2  2  2  4  4  6  0  4  8  6 10  0  0 14  6  8  8  4  4  6  2  6 10  4 12  6  2  2  4  2  2 10  4  2  8  6  6  6  6  8  2  6 14
 0  0  0  8  0  0  0  0  0  8  8  0  0  0  0  8  8  8  8  0  8  0  8  8  8  8  0  8  8  0  0  8  8  8  8  0  0  0  0  0  8  8  8  0  8  0  8  8
 0  0  0  0  8  0  0  0  0  8  0  0  0  8  0  0  0  0  0  0  0  8  8  8  8  8  8  8  8  8  8  0  8  0  8  8  8  8  0  0  0  0  8  0  8  0  0  0
 0  0  0  0  0  8  0  0  0  0  8  8  8  8  0  0  8  0  0  8  0  8  8  8  8  0  0  0  0  8  8  8  8  0  8  0  0  0  8  8  8  8  0  0  8  0  0  8
 0  0  0  0  0  0  8  0  0  8  8  0  0  0  8  8  8  8  0  0  8  0  8  8  8  8  8  0  0  8  8  0  0  0  8  0  8  8  0  8  0  8  0  0  0  8  8  0
 0  0  0  0  0  0  0  8  8  0  0  0  8  0  8  8  0  8  8  8  0  8  8  0  0  8  8  8  8  0  0  0  0  0  8  0  0  8  0  0  8  0  8  8  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+186x^40+172x^41+916x^42+1076x^43+3335x^44+4204x^45+8178x^46+8900x^47+11638x^48+8884x^49+8334x^50+4188x^51+3181x^52+1060x^53+834x^54+172x^55+192x^56+16x^57+38x^58+19x^60+4x^62+7x^64+1x^68

The gray image is a code over GF(2) with n=384, k=16 and d=160.
This code was found by Heurico 1.16 in 33 seconds.