The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+116x^45+223x^46+528x^47+667x^48+782x^49+1299x^50+1364x^51+1052x^52+724x^53+575x^54+342x^55+183x^56+198x^57+71x^58+32x^59+12x^60+4x^61+6x^62+6x^63+4x^64+2x^66+1x^72

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 1.06 seconds.