The generator matrix

 1  0  1  1  6  1  4  1  1  1  1  2  1  1 14  0  1  1  1  1 14  1 12  1  1  1  1  1 10  4  1  1  1  8  1  6  1 12  2  1  4 12 12  1  1 10  1  1  2  2  1
 0  1  1  6  1  7  1  4  5  3 10  1 14 11  1  1  1  6 13  2  1 12  1 11  8 14 11 13  1  1  3 12  1  1 15  1  9  2  4 14  4  1  2  3  3  1  7 15  2  2  9
 0  0  2  0  0  2 10 10  8  8 14 10  4  2 10  6 12 14  2 12  4  6  8  4 12  2  4  6  6 12 14  0 12  4  6  4  8  6  6  8  2  0 10 12 14  8 12  6  2 14  6
 0  0  0  8  0  0  8  0  8  0  8  0  8  0  0  8  8  8  8  0  8  0  8  0  8  0  0  0  0  8  8  8  8  0  8  8  8  8  0  0  0  8  8  8  8  0  8  0  0  8  0
 0  0  0  0  8  0  0  0  0  8  8  8  8  8  0  8  8  0  0  8  0  0  8  8  0  8  0  8  8  0  8  8  8  0  0  8  0  0  0  0  8  8  8  0  0  0  8  8  0  0  0
 0  0  0  0  0  8  8  8  0  0  8  8  0  8  8  8  0  8  0  0  0  0  8  8  8  0  8  0  0  8  0  8  8  0  8  0  8  0  0  8  0  0  0  8  0  8  0  0  8  8  8

generates a code of length 51 over Z16 who´s minimum homogenous weight is 45.

Homogenous weight enumerator: w(x)=1x^0+144x^45+321x^46+1126x^47+1055x^48+2354x^49+2078x^50+2724x^51+1862x^52+2194x^53+961x^54+820x^55+290x^56+286x^57+57x^58+60x^59+22x^60+14x^61+6x^62+6x^63+2x^64+1x^66

The gray image is a code over GF(2) with n=408, k=14 and d=180.
This code was found by Heurico 1.16 in 3.46 seconds.