The generator matrix

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

generates a code of length 49 over Z16 who´s minimum homogenous weight is 40.

Homogenous weight enumerator: w(x)=1x^0+203x^40+44x^41+406x^42+400x^43+1576x^44+2224x^45+5084x^46+7280x^47+10109x^48+10824x^49+10172x^50+7280x^51+5244x^52+2224x^53+1384x^54+400x^55+455x^56+44x^57+94x^58+56x^60+12x^62+14x^64+4x^68+2x^72

The gray image is a code over GF(2) with n=392, k=16 and d=160.
This code was found by Heurico 1.16 in 37.9 seconds.