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  2  1  1  2  1  4  4  2  1  1  4  1  4  2  1  2  1  1  4  4  1  2
 0 12  0  0  0  4 12  4  8  0  4  0  8  4  4  4  4  0 12  0  4  0  4  8  4  0  0  4  4  8 12  8  0 12  8  0 12  4 12  8  0  4  0  0  8  0  8  8  4  0
 0  0 12  0  4  4 12  0  0  4  8  0 12 12  8  4  4  0  8  4  0  4  0  8  4  8  4 12  0  0 12 12 12 12  0  0  8  8  0 12  4  4 12 12 12  8  4  4  0  8
 0  0  0 12  4  0 12  4  4  8  0  8  4  4  4  8  8  0 12  4  0  4  8  0 12  4  4  0 12 12  4 12  4  4  4 12 12  4  8  0 12  0  0  4  8  4  0  8  4  0
 0  0  0  0  8  0  0  8  0  8  8  0  0  0  0  8  0  0  8  0  8  0  8  8  0  8  0  8  0  8  8  0  8  8  8  8  8  8  0  0  0  0  0  8  8  0  0  0  0  8
 0  0  0  0  0  8  0  8  8  8  0  8  8  0  8  8  0  8  8  0  8  0  0  8  8  0  8  8  8  0  8  8  8  8  0  0  0  8  0  0  0  0  8  0  0  8  8  8  0  8
 0  0  0  0  0  0  8  0  8  8  8  0  0  0  0  0  0  8  8  8  8  0  0  8  0  8  8  0  8  8  0  8  0  8  0  8  8  8  0  8  0  0  0  0  0  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+109x^42+279x^44+52x^45+467x^46+488x^47+897x^48+988x^49+1704x^50+1008x^51+881x^52+492x^53+412x^54+40x^55+189x^56+4x^57+99x^58+47x^60+25x^62+8x^64+1x^68+1x^72

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 1.3 seconds.