The generator matrix

 1  0  1  1  1  4  1  1 14  1  1  2  8  1  0  1  1  1  6  1  1  6  1  0  1  1  1  4  1  1  2 10  1  1 14  1  0  2  1  2  6  6  8  8  4  4  1  1
 0  1  1  0  3  1  6  5  1  2  7  1  1 12  1  8 15  3  1 13  6  1 13  1  1 11 10  1  2  7 10  1 12 11  1  4  0  2 12  0  1  1  8  4  1  1  5  6
 0  0  2  6  0  2  0  8  4 14  2  2  4  2 14  4  8  6 14  2 10  4  0  2  6 14 12  8  8  8  2  6  0 12  6  8  2  2  2 14  6  8  2  2  0  6 14  4
 0  0  0 12  0  0  0  0  0  4  8  8  0  4  0  8  8  8  8  0 12 12 12 12 12  4  4  4 12 12 12 12  8  0 12  4  0  8  4 12 12  0  4 12  4 12  8 12
 0  0  0  0  8  0  0  8  0  0  0  0  8  8  8  8  0  8  8  8  8  0  8  0  8  0  0  8  0  0  0  8  0  8  0  8  8  8  0  8  8  8  8  8  0  8  0  8
 0  0  0  0  0  8  0  0  0  0  0  8  0  0  8  0  0  0  8  0  0  0  8  8  8  8  8  8  0  0  0  0  8  8  8  0  8  0  8  8  8  8  0  0  8  8  0  8
 0  0  0  0  0  0  8  8  8  8  8  8  8  8  8  8  8  8  0  0  0  8  8  8  8  0  8  8  8  0  0  0  0  8  0  0  0  0  8  8  0  8  0  0  0  8  8  0

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

Homogenous weight enumerator: w(x)=1x^0+93x^40+368x^41+580x^42+1848x^43+2306x^44+6234x^45+5652x^46+11216x^47+8306x^48+12208x^49+5838x^50+5834x^51+2148x^52+1880x^53+546x^54+286x^55+61x^56+40x^57+46x^58+14x^59+10x^60+6x^61+10x^62+2x^63+3x^64

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 33.6 seconds.