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  8  8  2  4  4  1  2  2  2  1  4  1  1 12  1  1  2  2  4  2  1  8  1  8  1  1  8  1
 0  2  0  0  0  2  6 14  4 12  6  2  2 10 12 12 12  8  2  0  2 10  8 14  4  2  2  4 12  2  0  2 10  8  8  4  2  4  2 14  8  8 12  2 10  4 12 14  8  8 14  0  0
 0  0  2  0  2  2  2  0  8 10  4 14  0  6  2 12  6  2 14  4  8 10  4  0 14  2  4 10  8  0  2  0 10  2  6  2 10  0  0  4  4  0 14  2 14 14  2  6  8 14  0 12  0
 0  0  0  2  2  0  2  2  2 10 12  8 14 10  8 12  0 14  4 14 10  2  4  4  8  0 14 10  2  4 12 10 10  0  2 14 12  8  0 10 10  2 10  6 10 10 14 14  2  0  0  2  0
 0  0  0  0  8  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  8  8  8  8  8  8  8  8  8  8  0  8  8  8  8  8  8  0  8  0  0  8  8  8  8  8  0  0  0  0
 0  0  0  0  0  8  0  0  8  8  8  0  8  8  8  8  8  0  8  8  8  0  8  8  0  8  0  0  8  0  0  8  0  8  8  8  8  0  8  8  0  0  8  8  8  0  0  0  0  8  0  0  0
 0  0  0  0  0  0  8  8  8  8  0  0  8  8  0  8  8  0  8  0  0  0  0  8  0  0  8  8  8  0  8  0  8  8  0  0  8  8  8  8  8  8  0  8  8  8  0  0  0  8  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+79x^44+360x^45+754x^46+1180x^47+2112x^48+2860x^49+4877x^50+6916x^51+8388x^52+10110x^53+8754x^54+6976x^55+5119x^56+2986x^57+1875x^58+984x^59+640x^60+302x^61+119x^62+68x^63+43x^64+18x^65+4x^66+4x^67+1x^68+4x^69+1x^70+1x^80

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 53.3 seconds.