The generator matrix

 1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  2  0  1  2  8  1  1  1  2  8  1  1  2 12  1  4  1  2  2  1  2  1  1  2  1  2  1  2  0  1  1  1  1  2  1
 0  2  0  6  0  6  0  2  4  6 12 10 12  2  4 14  6  6  2  0 14  2  8 14  2  6  2 12  8 10  2  8  2  6  2 14  4  0  6  8  4 14 10  6  0  2  4 14  8 12 14  0
 0  0 12  0  0  4  4  4  4  0  8  4 12  8  0  4  0  0  8  0  4 12  0 12  8 12  0  8  8  0  4  4  4 12  4  0  0  8  8  4  4  0  0  4  8  4  4  8  8  0  0  0
 0  0  0 12 12  4  4  0  8  8  8  4 12 12  4  8  8  0  8  8  0  0  4  0  4 12 12  0 12  0  4 12  0  0  0 12  0  4  0 12  4  0  8  4 12 12  0  4  4 12  4  0
 0  0  0  0  8  0  0  0  8  8  8  0  8  0  0  0  8  8  0  0  8  8  0  8  8  8  8  8  0  0  0  0  0  8  8  0  0  0  8  8  0  0  0  8  8  8  0  0  8  0  8  0
 0  0  0  0  0  8  0  0  0  0  8  0  8  0  0  8  8  8  8  0  8  0  8  0  0  8  8  0  0  8  0  8  0  0  8  0  8  8  0  8  8  0  8  8  0  0  8  8  0  8  8  0
 0  0  0  0  0  0  8  0  0  8  0  8  0  8  8  0  8  0  0  0  8  8  0  0  8  8  0  0  0  8  0  8  8  0  0  0  0  8  8  0  8  0  8  8  0  8  8  0  8  0  8  0
 0  0  0  0  0  0  0  8  8  8  8  8  0  8  0  0  8  0  8  8  0  0  0  8  8  8  0  8  0  8  0  8  8  0  8  8  8  0  0  8  0  8  0  8  8  8  8  8  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+47x^42+110x^43+215x^44+288x^45+593x^46+622x^47+1548x^48+1966x^49+3983x^50+4152x^51+5700x^52+4216x^53+3991x^54+2032x^55+1551x^56+588x^57+520x^58+218x^59+169x^60+104x^61+69x^62+34x^63+27x^64+6x^65+9x^66+4x^68+3x^70+1x^72+1x^74

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.