The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+52x^45+163x^46+386x^47+738x^48+802x^49+1396x^50+1134x^51+1513x^52+810x^53+591x^54+322x^55+168x^56+58x^57+20x^58+10x^59+6x^60+2x^61+5x^62+4x^63+5x^64+4x^65+1x^68+1x^70

The gray image is a code over GF(2) with n=408, k=13 and d=180.
This code was found by Heurico 1.16 in 0.816 seconds.