The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+28x^42+40x^43+221x^44+356x^45+799x^46+1568x^47+2791x^48+4988x^49+7436x^50+9248x^51+10309x^52+9632x^53+7349x^54+5184x^55+2856x^56+1344x^57+692x^58+344x^59+175x^60+60x^61+73x^62+22x^64+4x^65+4x^66+7x^68+3x^70+2x^72

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 35.3 seconds.