The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+18x^42+214x^43+292x^44+1040x^45+1065x^46+2996x^47+3047x^48+5574x^49+4496x^50+5458x^51+3097x^52+2886x^53+966x^54+1006x^55+258x^56+226x^57+38x^58+48x^59+18x^60+2x^61+9x^62+6x^63+6x^64+1x^68

The gray image is a code over GF(2) with n=400, k=15 and d=168.
This code was found by Heurico 1.16 in 9.12 seconds.