The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+127x^44+294x^45+583x^46+766x^47+1264x^48+1660x^49+2387x^50+2268x^51+2490x^52+1688x^53+1164x^54+740x^55+482x^56+184x^57+143x^58+60x^59+45x^60+10x^61+8x^62+6x^63+5x^64+4x^65+2x^66+2x^68+1x^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 3.89 seconds.