The generator matrix

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

generates a code of length 50 over Z16 who´s minimum homogenous weight is 41.

Homogenous weight enumerator: w(x)=1x^0+24x^41+123x^42+378x^43+578x^44+1032x^45+1443x^46+2832x^47+3200x^48+4920x^49+3698x^50+4964x^51+3231x^52+2920x^53+1446x^54+992x^55+372x^56+304x^57+175x^58+50x^59+36x^60+16x^61+23x^62+3x^64+4x^66+3x^68

The gray image is a code over GF(2) with n=400, k=15 and d=164.
This code was found by Heurico 1.16 in 14.8 seconds.