The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+33x^42+94x^43+170x^44+314x^45+530x^46+1000x^47+1265x^48+3076x^49+2433x^50+5778x^51+3374x^52+5852x^53+2592x^54+2934x^55+1183x^56+1022x^57+503x^58+272x^59+118x^60+96x^61+46x^62+26x^63+30x^64+6x^65+7x^66+8x^67+2x^68+2x^69+1x^72

The gray image is a code over GF(2) with n=416, k=15 and d=168.
This code was found by Heurico 1.16 in 16.3 seconds.