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

generates a code of length 50 over Z16 who´s minimum homogenous weight is 42.

Homogenous weight enumerator: w(x)=1x^0+109x^42+8x^43+240x^44+32x^45+471x^46+424x^47+800x^48+1088x^49+1990x^50+1048x^51+770x^52+416x^53+374x^54+56x^55+180x^56+105x^58+53x^60+19x^62+3x^64+4x^66+1x^76

The gray image is a code over GF(2) with n=400, k=13 and d=168.
This code was found by Heurico 1.16 in 3.23 seconds.