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

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

Homogenous weight enumerator: w(x)=1x^0+84x^41+122x^42+182x^43+306x^44+370x^45+788x^46+1054x^47+1705x^48+2468x^49+2384x^50+2350x^51+1758x^52+1082x^53+684x^54+310x^55+278x^56+186x^57+102x^58+68x^59+47x^60+28x^61+16x^62+4x^63+6x^65+1x^76

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 9.73 seconds.