The generator matrix

 1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  2  0  1  1  2 12  1  1  2  1  0  1  2  1 12  2  1  1  1  2  0  1  1  1 12  2  1  1  0  0  1 12  4  1  4
 0  2 12  6  0  6 12 10  0  6 12 10  0  6 12  6  2 10  0 10  2  6 12  6 10  2 10 10 12  2  6  6 10  0 10  2  0  0  6  2  6  8 12  2  2 10  2 12  6  0
 0  0  8  0  0  0  0  0  0  0  0  0  8  0  0  0  0  0  8  8  8  0  8  8  8  0  8  0  8  8  0  0  8  0  8  8  8  8  8  8  8  8  0  8  0  8  8  0  0  8
 0  0  0  8  0  0  0  0  0  0  0  0  0  8  0  0  0  0  0  0  0  8  0  0  0  0  8  8  0  8  8  8  8  8  8  8  8  8  8  0  8  0  0  0  8  0  0  8  8  8
 0  0  0  0  8  0  0  0  0  0  8  0  8  0  0  0  8  8  8  8  0  8  0  0  8  0  8  8  8  0  0  0  0  0  8  8  0  0  8  8  0  8  8  0  8  0  0  8  8  8
 0  0  0  0  0  8  0  0  0  0  0  0  0  8  0  8  0  8  0  0  0  0  0  8  8  8  8  0  0  8  0  8  8  8  0  8  0  8  8  8  0  8  8  8  0  8  0  0  0  0
 0  0  0  0  0  0  8  0  0  0  0  0  8  0  8  8  8  0  0  0  8  0  0  0  8  0  8  0  8  8  0  8  0  8  0  0  8  8  0  0  0  8  8  8  8  8  8  8  0  8
 0  0  0  0  0  0  0  8  0  0  0  8  0  0  8  0  0  8  8  8  0  8  8  8  0  8  8  8  0  8  0  0  8  8  8  0  0  0  8  8  0  0  0  8  8  0  8  8  8  8
 0  0  0  0  0  0  0  0  8  0  8  0  8  0  8  8  0  0  8  0  8  0  8  8  0  8  0  8  0  0  0  0  0  0  8  0  0  8  8  0  8  8  0  0  8  0  0  8  8  8
 0  0  0  0  0  0  0  0  0  8  0  8  0  0  8  0  0  8  8  8  8  0  0  8  8  0  8  8  8  0  8  8  8  0  0  8  0  0  0  0  0  0  8  8  0  8  0  0  8  0

generates a code of length 50 over Z16 who´s minimum homogenous weight is 40.

Homogenous weight enumerator: w(x)=1x^0+169x^40+20x^41+142x^42+172x^43+619x^44+864x^45+1340x^46+2592x^47+3577x^48+4520x^49+4724x^50+4568x^51+3601x^52+2624x^53+1328x^54+832x^55+547x^56+164x^57+142x^58+28x^59+141x^60+4x^62+42x^64+7x^68

The gray image is a code over GF(2) with n=400, k=15 and d=160.
This code was found by Heurico 1.16 in 27.5 seconds.