The generator matrix

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

generates a code of length 51 over Z16 who´s minimum homogenous weight is 44.

Homogenous weight enumerator: w(x)=1x^0+48x^44+160x^45+310x^46+712x^47+1144x^48+2146x^49+2104x^50+3264x^51+2080x^52+2102x^53+1130x^54+654x^55+284x^56+120x^57+32x^58+28x^59+24x^60+14x^61+6x^62+14x^63+3x^64+2x^65+2x^70

The gray image is a code over GF(2) with n=408, k=14 and d=176.
This code was found by Heurico 1.16 in 2.66 seconds.