The generator matrix

 1  0  1  1  1  6  1  1  8  1 14  1  1  1  8 10  1  1  1  1 14  1  1 12  0  1  1  1  1  1  1 12  1  1  2  1  8  1  1  1 12  4  1 12 14  1  2  2  0  1  1  8 12
 0  1 11  6 13  1  0 11  1  6  1 13 12  7  1  1  5 14  2  9  1  3  6  1  1  4  0 15  1  8  3  1  9 15  1 10  1  3  2  1  1  1 15  1  1  5  1  4  1 10 15  1  1
 0  0 12  0  4  0  0  0  8  0  8  8  0  4  4 12  0  4 12  4  4  8  4  4  4  8  4  0  8  0  4  8 12  4  0 12  4  4  8  0  4  8 12  8  4  0 12  8  8  4  8  8  0
 0  0  0 12  0  0 12  4 12  8  4 12  0  8  0  4  8  0  0 12  8  0 12  4 12 12  4  8 12  4  4  8 12 12  4  4  0  4  4  4 12  0  4  0  8  8  0  4  8  4  0 12  0
 0  0  0  0  8  0  0  0  0  0  0  0  0  8  0  0  8  8  8  8  0  8  8  0  0  0  8  8  0  0  0  8  8  8  8  0  0  0  8  0  0  8  8  8  0  0  8  8  0  8  8  0  0
 0  0  0  0  0  8  0  0  0  8  0  0  0  0  0  8  8  8  8  8  0  0  0  8  8  8  8  0  8  0  0  8  0  0  0  8  8  8  0  0  0  8  0  0  0  0  8  8  8  8  8  8  8
 0  0  0  0  0  0  8  0  0  0  8  8  8  8  0  0  0  8  0  8  8  8  0  8  0  8  0  8  8  8  8  8  0  8  8  8  8  0  0  0  8  0  0  8  8  8  8  8  0  8  8  0  0
 0  0  0  0  0  0  0  8  0  0  0  8  0  0  8  8  8  8  8  0  8  8  8  0  0  8  0  0  0  8  8  0  8  0  8  0  0  8  0  0  8  0  0  0  0  8  0  0  0  8  8  8  8

generates a code of length 53 over Z16 who´s minimum homogenous weight is 44.

Homogenous weight enumerator: w(x)=1x^0+190x^44+52x^45+470x^46+352x^47+1742x^48+2108x^49+5154x^50+6812x^51+10984x^52+10004x^53+10712x^54+6828x^55+5421x^56+2132x^57+1440x^58+340x^59+511x^60+40x^61+130x^62+4x^63+83x^64+14x^66+10x^68+1x^72+1x^76

The gray image is a code over GF(2) with n=424, k=16 and d=176.
This code was found by Heurico 1.16 in 44.6 seconds.