The generator matrix

 1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  0  4  2  2  1  1  2  1  4  1  8  2  1  1  1 12  1  8  0  1 12  1  1  2  1  1  1  2  2  2  1  1
 0  2  0  0  0  2 14  2  4  2 12  2 10  8  2  4 14  4 14  0 12 12 14 12 10 10  2  2  8  2 14  0 12  8  8  6  8  2  6  8  8 14 14  2 12 14  8  2  6  4  0
 0  0  2  0  2  2  2  8 14  6  8  0 14 12 12 10  6  2  0  2  4 10 12  0  6 10  8 14  6 12  0  6  4 12  2  8  2 10  6  2 10  0 12 14  2 12  8  6  4  0  0
 0  0  0  2  2  0 10  2  0  8  8  8 10 14 14  2  4  8 12  2  2 12  0  6 14  0  4  6 12  6 12 10  2  8 10  2  0  0  6  4 14  8 12  2  6 10 14  0  4  0  0
 0  0  0  0  4  0  4  0 12 12 12  4  8  4 12  0  0  8  8 12 12 12  0  0  8 12  8 12  4  0 12 12  4  4  4  4  8 12 12  4  4 12  4  4  4  8  4  0  0  4  0
 0  0  0  0  0  8  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  8  8  8  8  8  8  8  8  8  8  8  8  8  8  8  8  8  0  0  8  8  8  8  8  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+76x^42+324x^43+680x^44+1158x^45+1846x^46+2774x^47+4528x^48+6876x^49+9359x^50+10404x^51+9065x^52+7080x^53+4798x^54+2738x^55+1625x^56+1096x^57+583x^58+262x^59+155x^60+42x^61+39x^62+8x^63+10x^64+4x^65+2x^66+2x^67+1x^70

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 50.9 seconds.