The generator matrix

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

generates a code of length 52 over Z16 who´s minimum homogenous weight is 44.

Homogenous weight enumerator: w(x)=1x^0+68x^44+158x^45+350x^46+418x^47+900x^48+870x^49+2256x^50+1662x^51+3186x^52+1630x^53+2182x^54+850x^55+866x^56+382x^57+303x^58+122x^59+82x^60+28x^61+28x^62+20x^63+17x^64+4x^65+1x^74

The gray image is a code over GF(2) with n=416, k=14 and d=176.
This code was found by Heurico 1.16 in 3.81 seconds.