The generator matrix

 1  0  0  1  1  1  2  1  1  1  1 14 14  6  2 12  1  1  2  1  1  0  1  1  1  8  1  1  6  0  1  1  1  2  0  4 10  6  1  0  1  1 12  1  1  1  4  0  8  1
 0  1  0  2  5  7  1  0 14  9  7  4  1  1  2  1  4  9  1 10  7  1  5 10  4  4 15  0  1  0  9  8 13  1  1  1  1  1 14  6 10 15  1  7  1  3  1  1  4  0
 0  0  1  1  3  2  1  6  7  5  4  1  2  3  1  5  7  6  4  0  7  6  0  6  1  1  5  5  0  1  3  7  1  2  3  7  3 14 11  1 10 11 12  8 13  6  5  5  1  0
 0  0  0  8  0  0  0  0  8  8  8  8  0  0  8  0  8  8  8  8  0  0  0  8  0  8  0  8  0  8  8  8  0  0  8  8  8  8  8  0  8  0  0  0  0  8  0  8  0  0
 0  0  0  0  8  0  0  0  0  8  0  0  8  8  8  0  8  8  8  8  0  8  0  0  8  8  8  0  0  0  0  8  8  0  8  8  0  0  0  0  8  0  8  8  8  8  0  8  0  0
 0  0  0  0  0  8  0  0  0  0  8  0  8  8  8  8  0  8  0  0  0  0  0  8  8  8  8  8  8  0  0  0  0  8  8  8  8  8  8  8  0  0  8  0  8  0  8  0  8  0
 0  0  0  0  0  0  8  8  8  0  0  0  0  8  0  0  8  8  8  8  0  0  8  0  8  8  0  0  0  8  8  0  8  8  0  8  8  0  8  0  0  8  8  0  8  8  8  0  0  0

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

Homogenous weight enumerator: w(x)=1x^0+28x^42+134x^43+760x^44+1666x^45+2768x^46+5382x^47+6764x^48+10728x^49+9106x^50+10900x^51+6830x^52+5284x^53+2613x^54+1476x^55+713x^56+232x^57+69x^58+22x^59+29x^60+10x^61+7x^62+6x^63+6x^64+1x^66+1x^68

The gray image is a code over GF(2) with n=400, k=16 and d=168.
This code was found by Heurico 1.16 in 27.3 seconds.