The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+105x^44+342x^45+751x^46+1224x^47+2219x^48+3094x^49+4817x^50+6588x^51+8917x^52+9240x^53+9001x^54+6786x^55+5162x^56+2916x^57+2011x^58+1134x^59+617x^60+330x^61+144x^62+70x^63+30x^64+14x^65+12x^66+6x^67+5x^68

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 53.9 seconds.