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

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

Homogenous weight enumerator: w(x)=1x^0+74x^41+160x^42+194x^43+269x^44+344x^45+556x^46+868x^47+1803x^48+2646x^49+2656x^50+2614x^51+1792x^52+878x^53+530x^54+310x^55+252x^56+128x^57+111x^58+104x^59+43x^60+26x^61+18x^62+6x^63+1x^74

The gray image is a code over GF(2) with n=400, k=14 and d=164.
This code was found by Heurico 1.16 in 14.9 seconds.