The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+41x^44+162x^45+454x^46+870x^47+1741x^48+2772x^49+4942x^50+7068x^51+9629x^52+9992x^53+9832x^54+7130x^55+5135x^56+2862x^57+1496x^58+624x^59+378x^60+202x^61+100x^62+44x^63+35x^64+10x^65+6x^66+8x^67+2x^70

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 37.8 seconds.