The generator matrix

 1  0  1  1  1 14  1  1  4  2  1  1  4  1  1  1  6  1  6  1  1 12  1  1  1  1  0  1  1 10  1  1  1  1  1  1  4  1  4  8  1  6  1 10 14  1  4  1  4 14  1
 0  1  1  6  7  1  3  4  1  1 14  5  1  5  0  7  1  8  1  3 14  1 11  6  3 10  1  4  7  1 15  9  0 13  8 12  1  6  2  1  6  1  1  1  1 12  1  2  1  1  7
 0  0  2  0 14  8  0 10 10  2 14 12  6  2 12  0  0 10  2  2  4  4 12  2 10 10 10  8  4 14  8 12 12  6  4  6  6  4  2  0 10 12 14  6 12 14  6 14  8 14  6
 0  0  0 12  0 12  8  0  8  8 12 12 12  4 12  4  8  0  4  8  0 12  0 12  4  4  4  4  0  0  0  4  4  4  8 12  0  0  8  4  0  8  8  4  8  8  4  0 12 12  4
 0  0  0  0  8  0  0  0  0  8  0  0  8  8  8  8  8  8  0  8  8  8  8  0  0  8  0  8  0  0  8  8  0  8  8  0  8  0  8  0  8  8  8  8  0  0  0  8  0  8  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+334x^46+826x^47+1347x^48+2020x^49+2293x^50+2690x^51+2383x^52+1904x^53+1243x^54+670x^55+255x^56+140x^57+54x^58+62x^59+9x^60+12x^61+10x^62+8x^63+5x^64+1x^66+1x^70

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 2.63 seconds.