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

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

Homogenous weight enumerator: w(x)=1x^0+65x^44+126x^45+254x^46+764x^47+757x^48+1710x^49+1983x^50+3848x^51+3655x^52+6476x^53+3636x^54+3998x^55+1908x^56+1770x^57+676x^58+574x^59+255x^60+156x^61+82x^62+30x^63+12x^64+19x^66+2x^67+1x^68+2x^69+4x^70+2x^72+2x^74

The gray image is a code over GF(2) with n=424, k=15 and d=176.
This code was found by Heurico 1.16 in 14.7 seconds.