The generator matrix

 1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  2  1  1  1  1  1  1  2  1  1  2  1  4  4  2  1  2  2  4  4  1  1  1  1  1  1  4  2
 0 12  0  0  0  4 12  4  0  8  0 12  0  0  4 12  8  4  0  0  4  4  0 12  4 12  4  8 12 12  0 12  0  4 12  8 12 12  0 12  8 12  0  0  8  4 12  4  4  0  4  4
 0  0 12  0  4  4 12  0  0  0 12  8  0 12 12  4  8  0 12 12  8 12 12  0 12 12  8  4 12  4  0  8  4  8  0  4  4  0  0  0  4 12  4 12 12 12  8 12  4  8  8  4
 0  0  0 12  4  0 12  4  0  4 12 12  8  8  8 12 12  8 12  8  0  0 12  0  8  4 12  8  4  0  4  8  8  4  8 12  4  0 12  4  0  4  4  8  4 12  4  0 12  8 12  0
 0  0  0  0  8  0  0  0  0  0  0  0  0  0  8  8  8  8  8  0  8  8  0  0  0  8  0  0  0  8  0  8  8  8  8  0  8  0  8  0  8  8  8  8  0  8  8  0  8  0  8  0
 0  0  0  0  0  8  0  0  0  0  8  8  8  0  0  0  0  0  0  0  8  8  0  8  0  0  8  8  0  0  8  8  8  8  8  0  0  8  0  0  0  8  8  0  8  8  8  0  0  8  8  8
 0  0  0  0  0  0  8  0  0  8  8  8  0  0  8  0  0  0  8  8  0  0  0  0  8  0  0  0  8  0  8  0  8  8  8  0  0  0  8  0  8  8  8  0  8  0  0  8  8  0  8  8
 0  0  0  0  0  0  0  8  0  0  0  0  0  0  0  0  0  8  8  8  8  8  8  0  8  8  0  8  8  0  8  0  8  0  8  0  8  8  0  0  8  8  0  0  8  0  8  0  8  8  0  8
 0  0  0  0  0  0  0  0  8  0  0  0  0  8  8  0  8  8  8  8  0  0  8  8  0  0  8  8  8  8  0  8  0  0  8  8  8  0  0  0  0  8  0  8  0  8  0  8  0  8  0  8

generates a code of length 52 over Z16 who´s minimum homogenous weight is 41.

Homogenous weight enumerator: w(x)=1x^0+58x^41+115x^42+188x^43+271x^44+286x^45+414x^46+664x^47+910x^48+2160x^49+3056x^50+4850x^51+6883x^52+4724x^53+3068x^54+2336x^55+906x^56+562x^57+400x^58+352x^59+194x^60+142x^61+102x^62+56x^63+38x^64+4x^65+12x^66+2x^67+11x^68+1x^74+1x^76+1x^80

The gray image is a code over GF(2) with n=416, k=15 and d=164.
This code was found by Heurico 1.16 in 56.2 seconds.