The generator matrix

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

generates a code of length 51 over Z16 who´s minimum homogenous weight is 48.

Homogenous weight enumerator: w(x)=1x^0+461x^48+588x^50+607x^52+304x^54+75x^56+4x^58+5x^60+2x^64+1x^80

The gray image is a code over GF(2) with n=408, k=11 and d=192.
This code was found by Heurico 1.16 in 93 seconds.