The generator matrix

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

generates a code of length 51 over Z16 who´s minimum homogenous weight is 40.

Homogenous weight enumerator: w(x)=1x^0+42x^40+194x^42+80x^43+453x^44+616x^45+1018x^46+3192x^47+3529x^48+9736x^49+7144x^50+13816x^51+6968x^52+9528x^53+3494x^54+3304x^55+1116x^56+600x^57+346x^58+88x^59+157x^60+78x^62+16x^64+12x^66+6x^68+2x^70

The gray image is a code over GF(2) with n=408, k=16 and d=160.
This code was found by Heurico 1.16 in 35.7 seconds.