The generator matrix

 1  0  1  1  1 14  1  1  0  1  1 14  1  1  0  1  6  1  1  2  1  1  1 12  1 14  1  1 10  8  1  1  1  1  0  1  1  6  4  4  2  1  1  1  1  1  8  6  8  1
 0  1 11  6  1  1  0  3  1  6  5  1 10  5  1 11  1  0  5  1  9  6  6  1 13  1  8 11  1  1  8  2  7  2  1  2 12  1  1  1 14  6 11 11  3 13  8  1  1  0
 0  0 12  0  0  0  0  4  4 12  0  4  8  4  0  4  4  4  8 12  4  8  4 12  8 12 12  8  0  0 12  8  4  4  8  4  8  8 12 12  0 12  4  8  4  8  4 12  0  0
 0  0  0 12  0  0  0  0  0  0  8  8  4  4 12  4 12  4 12  8 12  8  0  4 12 12  8 12  8 12 12  8  0 12  8 12  0  8 12  8  0  4  0  0  0  4  4  0  4  0
 0  0  0  0  4  4 12  4  4  4  8  0 12  8  4 12  8  0  4  0  0  0 12  8  8 12  0  8  0  0  4  4  8  4  8 12  8  0 12  4  4  0  8  0  0  8  8 12  0  0
 0  0  0  0  0  8  0  0  8  0  0  8  0  0  8  0  0  8  8  0  8  8  8  8  0  0  0  0  8  8  0  8  8  8  0  8  0  8  0  8  0  0  8  8  0  8  0  0  0  0
 0  0  0  0  0  0  8  8  8  0  8  0  8  0  0  8  8  0  8  8  8  8  8  0  8  0  0  0  8  0  8  0  0  0  8  8  8  0  8  8  0  8  8  0  8  8  8  0  8  0

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

Homogenous weight enumerator: w(x)=1x^0+46x^40+68x^41+183x^42+372x^43+677x^44+1176x^45+2974x^46+4972x^47+7200x^48+10002x^49+10375x^50+9510x^51+7774x^52+5030x^53+2640x^54+1190x^55+615x^56+334x^57+193x^58+78x^59+61x^60+26x^61+18x^62+6x^63+9x^64+4x^65+1x^66+1x^72

The gray image is a code over GF(2) with n=400, k=16 and d=160.
This code was found by Heurico 1.16 in 36.5 seconds.