The generator matrix

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

generates a code of length 49 over Z16 who´s minimum homogenous weight is 40.

Homogenous weight enumerator: w(x)=1x^0+58x^40+284x^41+497x^42+1462x^43+1444x^44+3702x^45+4075x^46+7712x^47+8269x^48+10374x^49+8243x^50+8124x^51+4156x^52+3600x^53+1402x^54+1200x^55+389x^56+332x^57+115x^58+62x^59+16x^60+10x^61+3x^62+2x^64+2x^65+1x^66+1x^72

The gray image is a code over GF(2) with n=392, k=16 and d=160.
This code was found by Heurico 1.16 in 47.6 seconds.