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

generates a code of length 50 over Z16 who´s minimum homogenous weight is 40.

Homogenous weight enumerator: w(x)=1x^0+224x^40+490x^42+12x^43+822x^44+148x^45+1586x^46+1532x^47+4137x^48+4452x^49+5992x^50+4452x^51+4144x^52+1532x^53+1576x^54+148x^55+826x^56+12x^57+414x^58+192x^60+54x^62+20x^64+2x^76

The gray image is a code over GF(2) with n=400, k=15 and d=160.
This code was found by Heurico 1.16 in 19.5 seconds.