The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+99x^40+50x^42+244x^44+96x^45+294x^46+480x^47+588x^48+1984x^49+560x^50+1984x^51+568x^52+480x^53+296x^54+96x^55+199x^56+78x^58+61x^60+2x^62+25x^64+6x^68+1x^76

The gray image is a code over GF(2) with n=400, k=13 and d=160.
This code was found by Heurico 1.16 in 1.38 seconds.