The generator matrix

 1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  2  1  0  1  1  1  1  1  2  1 12  1  1  2  1  0  1  1  1  2  1  1 12  2  1  0  1  2  0  0  2  1  1
 0  2 12  6  0  6 12 10  0  6 12 10  4 10  0  8  6  6 14  2  6 12  0 10 12 10 10  2 10  2  6 12  2  6  6 10 10 12  0  2  6  4  2 10 10  2  2  6  0  0
 0  0  8  0  0  0  0  0  0  0  8  0  0  0  8  8  8  0  8  8  8  0  8  0  0  8  0  8  8  8  0  0  8  8  0  8  8  0  0  0  0  8  8  8  8  8  0  8  0  0
 0  0  0  8  0  0  0  0  0  8  8  0  8  0  8  8  0  8  0  8  8  8  0  0  8  0  8  0  0  8  8  0  8  8  8  8  0  8  0  0  8  8  8  0  0  0  8  0  0  8
 0  0  0  0  8  0  0  0  8  0  0  0  0  0  8  8  0  0  0  0  0  0  0  8  8  8  8  8  8  8  8  8  8  0  8  0  8  8  0  0  0  8  0  8  8  0  8  0  0  8
 0  0  0  0  0  8  0  0  0  8  0  8  0  8  8  8  8  0  0  0  8  0  8  0  8  8  8  0  0  8  8  8  0  8  0  0  8  0  8  8  0  0  0  8  0  0  0  0  8  0
 0  0  0  0  0  0  8  0  8  0  8  8  0  8  0  8  8  8  8  0  0  0  0  8  0  0  8  0  8  8  8  0  0  8  0  0  8  8  0  8  8  8  8  8  0  0  0  8  0  0
 0  0  0  0  0  0  0  8  0  0  0  8  0  0  0  0  8  8  8  8  8  8  0  0  8  0  8  8  0  8  0  8  8  0  0  0  8  8  0  0  0  0  8  8  0  0  8  8  8  0

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

Homogenous weight enumerator: w(x)=1x^0+36x^42+20x^43+185x^44+188x^45+309x^46+596x^47+912x^48+1244x^49+1246x^50+1244x^51+902x^52+596x^53+292x^54+188x^55+159x^56+20x^57+26x^58+7x^60+7x^62+7x^64+4x^66+2x^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 1.15 seconds.