The generator matrix

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

generates a code of length 52 over Z16 who´s minimum homogenous weight is 42.

Homogenous weight enumerator: w(x)=1x^0+57x^42+70x^43+195x^44+374x^45+631x^46+1302x^47+2437x^48+5140x^49+7003x^50+10520x^51+10109x^52+10534x^53+7006x^54+5174x^55+2396x^56+1290x^57+612x^58+312x^59+197x^60+60x^61+43x^62+28x^63+20x^64+10x^65+7x^66+2x^67+3x^68+2x^72+1x^74

The gray image is a code over GF(2) with n=416, k=16 and d=168.
This code was found by Heurico 1.16 in 38.5 seconds.