The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+58x^46+202x^47+405x^48+516x^49+593x^50+638x^51+550x^52+496x^53+357x^54+180x^55+67x^56+10x^57+8x^58+2x^59+2x^62+2x^63+1x^64+2x^65+4x^66+1x^70+1x^74

The gray image is a code over GF(2) with n=408, k=12 and d=184.
This code was found by Heurico 1.16 in 0.241 seconds.