The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+66x^42+162x^43+311x^44+410x^45+848x^46+1010x^47+2028x^48+1998x^49+2774x^50+2058x^51+1992x^52+1034x^53+829x^54+306x^55+242x^56+122x^57+78x^58+44x^59+33x^60+20x^61+10x^62+4x^63+1x^64+2x^66+1x^70

The gray image is a code over GF(2) with n=400, k=14 and d=168.
This code was found by Heurico 1.16 in 4.27 seconds.