The generator matrix

 1  0  1  1  6  1  1  1  6  1 12  1  1  8  1 12  1  1  1  2  1  1  1  0  1  1  1  1 12  1  1  8  1 10  1  1  1  8  1  2  1  1  6  1  1 10  1  1  2  1  1
 0  1  1  6  1  3  5  4  1  2  1  7 13  1  4  1  6 13 10  1  2  3 12  1  7  6 15  5  1  0 15  1 12  1  2  6 13  0  2 14 14  4  1  1 10  1 12  2  1 13 11
 0  0  2  0  0  8  8 10  6 10 14 10  2  4 12  2 12  4  6  4  4 14  6  6  4  6  6  8  4  0  0 12 10  2  8  2 12  2 12  2  0 14  6 12 10  0  6  2  0  8  4
 0  0  0  8  0  8  0  0  8  8  0  0  8  8  8  8  8  0  0  8  0  8  8  8  8  8  0  8  0  0  8  0  8  0  0  0  0  0  0  8  0  0  0  8  8  0  0  0  8  8  8
 0  0  0  0  8  0  8  0  0  8  8  8  0  0  8  8  0  0  8  8  8  8  0  8  8  8  0  8  0  8  8  8  8  8  8  8  8  0  0  8  0  0  0  0  0  0  8  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+98x^46+464x^47+951x^48+848x^49+1339x^50+960x^51+1415x^52+742x^53+760x^54+320x^55+116x^56+100x^57+37x^58+16x^59+12x^60+6x^61+5x^62+1x^68+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 0.757 seconds.