The generator matrix

 1  0  1  1  1 14  1  4  1 10  1  1  1  6  1  2  1  1  1  0  1  1  1  4  1  1  1  1  6 12  1  1  1  0 10  1  1  1  1 10  1 12  0  1  8  1  1  1  1  1  1
 0  1  1  6  3  1 13  1  4  1 10 15  1  1  2  1 12  5  0  1  3  6  7  1  9  2 12  9  1  1  7  7  0  1  1 12 13  2  7  1  2  1  1 12  4  2 12  3  3 13  4
 0  0  2  0  8  8  0 14  6 14  6 10  8 10  4  4 12  6  2  2 14  4 12  0 10 14  6  4  0 12  8  6 12 14  4 10 12  2 10  2  8  8 14  4  2  2 12  8 12  0  2
 0  0  0 12  0  4  4 12  4  8  8  4 12  8 12  4  0  0 12  4  0  4  8 12  4  4  8 12  0  4  4  4 12  4  0  0  8  4  8 12  0  8  8  4  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+103x^46+430x^47+814x^48+1102x^49+1125x^50+1262x^51+1132x^52+1010x^53+602x^54+336x^55+128x^56+62x^57+34x^58+18x^59+12x^60+2x^61+12x^62+2x^63+1x^64+3x^66+1x^70

The gray image is a code over GF(2) with n=408, k=13 and d=184.
This code was found by Heurico 1.16 in 0.728 seconds.