The generator matrix

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

generates a code of length 52 over Z16 who´s minimum homogenous weight is 44.

Homogenous weight enumerator: w(x)=1x^0+36x^44+130x^45+330x^46+832x^47+1541x^48+2612x^49+3874x^50+4374x^51+5388x^52+4494x^53+3924x^54+2500x^55+1384x^56+706x^57+304x^58+152x^59+86x^60+56x^61+10x^62+12x^63+10x^64+2x^65+6x^66+2x^67+2x^68

The gray image is a code over GF(2) with n=416, k=15 and d=176.
This code was found by Heurico 1.16 in 9.66 seconds.