The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+428x^45+1852x^46+3230x^47+5716x^48+7436x^49+9180x^50+9450x^51+10139x^52+7480x^53+5414x^54+2812x^55+1535x^56+566x^57+168x^58+58x^59+33x^60+24x^61+10x^62+2x^63+2x^65

The gray image is a code over GF(2) with n=408, k=16 and d=180.
This code was found by Heurico 1.16 in 28.6 seconds.