The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+250x^46+296x^47+807x^48+908x^49+1304x^50+1184x^51+1241x^52+904x^53+768x^54+280x^55+167x^56+12x^57+38x^58+13x^60+2x^62+9x^64+6x^66+2x^68

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 19.9 seconds.