The generator matrix

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

generates a code of length 51 over Z16 who´s minimum homogenous weight is 46.

Homogenous weight enumerator: w(x)=1x^0+264x^46+850x^47+1626x^48+2112x^49+2563x^50+2162x^51+2367x^52+1808x^53+1295x^54+686x^55+371x^56+144x^57+61x^58+30x^59+17x^60+16x^61+9x^62+2x^64

The gray image is a code over GF(2) with n=408, k=14 and d=184.
This code was found by Heurico 1.16 in 1.98 seconds.