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

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

Homogenous weight enumerator: w(x)=1x^0+59x^40+60x^41+139x^42+172x^43+263x^44+294x^45+556x^46+780x^47+1738x^48+2802x^49+2699x^50+2794x^51+1786x^52+790x^53+522x^54+282x^55+195x^56+122x^57+141x^58+66x^59+47x^60+28x^61+33x^62+2x^63+7x^64+5x^66+1x^78

The gray image is a code over GF(2) with n=400, k=14 and d=160.
This code was found by Heurico 1.16 in 5.2 seconds.