The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+36x^44+110x^45+173x^46+326x^47+403x^48+850x^49+1137x^50+1996x^51+1894x^52+2734x^53+1820x^54+1910x^55+1091x^56+830x^57+399x^58+346x^59+128x^60+76x^61+45x^62+28x^63+24x^64+8x^65+7x^66+2x^67+6x^68+2x^70+1x^72+1x^74

The gray image is a code over GF(2) with n=424, k=14 and d=176.
This code was found by Heurico 1.16 in 4.57 seconds.