The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+54x^42+82x^43+221x^44+252x^45+653x^46+676x^47+1701x^48+2036x^49+3982x^50+4160x^51+5230x^52+4116x^53+4067x^54+2020x^55+1584x^56+680x^57+614x^58+194x^59+225x^60+72x^61+64x^62+32x^63+30x^64+12x^65+5x^66+4x^67+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.