The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+43x^40+130x^41+333x^42+792x^43+1328x^44+3062x^45+4479x^46+8352x^47+8676x^48+11102x^49+8698x^50+8554x^51+4501x^52+2974x^53+1254x^54+690x^55+267x^56+136x^57+73x^58+38x^59+26x^60+4x^61+11x^62+6x^63+5x^64+1x^68

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 32.7 seconds.