The generator matrix

 1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  2  8  0  8  2  1  2  1  1  1  1  1  0  2  2  1  0  2  1 12  2  4  1  1 12  8  1  1  1  2  1
 0  2  0  6  0  6  4  2  4 14  2  8  6 14 12  4 14  8  2  4 14  2  2  2  6  8 14  2 10  0  4 14  2 14 10  8  2 10  4  2 10 12  6  8  2  2  8  6  6  0  6
 0  0 12  0  0  0  4  8  0  4  4 12  8  4  4  4  8 12 12  0 12  4  0  8  8 12  0  0  4  4 12 12  4  8  4  0 12 12  0  0  4  8 12  0  0  0 12  8  4  8 12
 0  0  0 12  0  0  0  4  8  4  4  0  4  4  4 12  8  4  8 12  0  0 12  8 12  4 12  0  8 12  8  4  0 12  8 12 12 12  0  8  8 12 12  4  4  8  4  4 12  0 12
 0  0  0  0 12  0  0  0  4  4 12  4 12  8  8 12 12  0  0  8  8  8 12  4 12  4  8 12 12  8  4 12 12  0  4  8  0  8  0  8  4  8  8  0  4  0 12 12  4  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  0  8  8  8  8  8  8  8  8  8  8  8  8  8  8  8  8  0  8  8  0  8  8  0  8  8  0  0
 0  0  0  0  0  0  8  8  8  0  8  0  8  8  0  0  0  8  0  8  8  0  0  8  0  8  0  8  8  8  0  0  0  8  8  0  8  0  0  8  0  8  8  0  8  8  0  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+143x^42+28x^43+484x^44+288x^45+1172x^46+1244x^47+2728x^48+3244x^49+4638x^50+4692x^51+4929x^52+3340x^53+2634x^54+1172x^55+1056x^56+292x^57+377x^58+32x^59+186x^60+4x^61+58x^62+23x^64+2x^66+1x^68

The gray image is a code over GF(2) with n=408, k=15 and d=168.
This code was found by Heurico 1.16 in 16.4 seconds.