The generator matrix

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

generates a code of length 51 over Z16 who´s minimum homogenous weight is 42.

Homogenous weight enumerator: w(x)=1x^0+45x^42+152x^43+314x^44+940x^45+1331x^46+2978x^47+5165x^48+7422x^49+9368x^50+9858x^51+9990x^52+7262x^53+4852x^54+3198x^55+1346x^56+730x^57+237x^58+190x^59+70x^60+30x^61+32x^62+8x^63+8x^64+6x^66+2x^68+1x^78

The gray image is a code over GF(2) with n=408, k=16 and d=168.
This code was found by Heurico 1.16 in 35.1 seconds.