The generator matrix

 1  0  1  1  1  4  1 10  1  1  6  1  1  4  2  1  1  1  1 14  1  4  1  1  1  8  1  1  1 14  6  1  1  2  1  1  8  2 12  1  1 14  1  4 12  2  8  1  1
 0  1  1  0 11  1 10  1  5  6  1  7 15  1  1  8  6  7  2  1 13  1  9 12  0  1  2 15  5  1  1 10 14 10 13 13  2 10  8  5  9  1  7  1  1  0  2 15  0
 0  0  2  6  4  6 10 10  0  0  8  2  2 10  2  0 12  8 14  4 12  8  4 12  6  6  0 12  2  0  6 14 12  2  4  0  6 10  2  6  6  2 14  0  4  4  0  2  0
 0  0  0 12  0  4 12  4  0  0  0  8  4  0  8  4 12  4 12  0  8 12  4  4  8  4 12 12  4 12  0  8  8 12  0  8  4  0 12 12  0  8  0  4  4  4 12  4  0
 0  0  0  0  8  0  0  0  8  0  0  0  0  0  0  0  0  8  8  8  8  8  8  8  0  8  8  0  8  0  8  8  8  0  0  0  0  0  0  8  0  8  8  8  8  8  0  8  0
 0  0  0  0  0  8  0  8  0  0  0  0  0  8  8  0  0  0  8  8  8  8  8  8  8  8  0  0  0  8  0  0  0  0  0  8  8  8  0  0  8  8  8  0  0  8  0  0  0
 0  0  0  0  0  0  8  8  8  8  8  8  0  0  8  0  8  8  8  0  8  0  8  0  8  8  8  0  8  8  8  0  8  0  8  0  8  0  8  0  0  8  8  0  8  8  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+45x^40+146x^41+343x^42+914x^43+1493x^44+3218x^45+4092x^46+8114x^47+8884x^48+11054x^49+8782x^50+8132x^51+4422x^52+3334x^53+1166x^54+716x^55+361x^56+152x^57+73x^58+42x^59+21x^60+16x^61+6x^62+2x^63+5x^64+2x^66

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 33.4 seconds.