The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+39x^42+176x^43+370x^44+716x^45+1476x^46+3160x^47+4312x^48+7730x^49+9223x^50+11152x^51+8983x^52+8140x^53+4630x^54+2784x^55+1251x^56+724x^57+321x^58+180x^59+77x^60+32x^61+18x^62+16x^63+12x^64+2x^65+5x^66+4x^67+2x^68

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 35.9 seconds.