The generator matrix

 1  0  1  1  1  6  1  1 12  1  1 10  1  1  0  6  1  1 12 10  1  1  1  1  1  1  0  6  1  1  1  1 12 10  1  6  1  1  1  1  1  1 10 10  1  1  1  0  1  1  1  1
 0  1  3  6  5  1 12  7  1 10  9  1  0  3  1  1  6  5  1  1 12 10 15  9  0  3  1  1  6  5 15 12  1  1  3  1 10  9  0  5 12  0  1  1  6  3  0  1  0  3  0  0
 0  0  8  0  0  0  0  0  0  0  0  0  0  8  8  8  0  8  8  8  0  0  0  8  8  0  0  8  0  0  8  0  0  8  0  8  8  8  0  0  8  0  8  0  0  8  0  0  8  8  0  0
 0  0  0  8  0  0  0  0  0  0  0  0  0  0  0  0  8  0  0  0  0  0  8  8  8  8  8  8  8  8  8  0  8  8  8  8  8  8  8  0  0  0  8  8  0  0  0  8  8  0  0  0
 0  0  0  0  8  0  0  0  0  0  0  0  0  0  0  0  0  8  0  0  8  8  0  0  8  8  8  8  8  8  0  8  8  0  8  0  8  0  8  8  0  8  8  0  8  0  8  8  0  8  0  0
 0  0  0  0  0  8  0  0  0  0  0  8  0  0  8  8  0  0  0  0  8  8  8  8  8  8  0  8  8  0  8  0  0  0  8  8  0  0  0  8  8  0  8  8  8  8  0  8  0  0  0  0
 0  0  0  0  0  0  8  0  0  0  0  8  8  0  0  8  8  0  8  8  0  8  0  0  0  8  0  0  8  8  0  0  8  0  8  8  8  0  0  0  0  0  8  0  8  8  8  8  8  8  0  0
 0  0  0  0  0  0  0  8  0  0  8  0  0  0  8  8  0  8  8  8  8  8  8  0  0  0  8  0  0  8  8  0  0  0  8  0  8  0  0  8  8  8  8  0  0  0  0  8  0  0  0  0
 0  0  0  0  0  0  0  0  8  0  8  8  0  8  8  0  8  0  8  0  8  0  8  8  0  0  0  0  8  8  0  0  0  8  0  0  0  0  8  8  0  0  8  0  8  8  8  8  8  8  0  0
 0  0  0  0  0  0  0  0  0  8  8  8  8  8  0  8  0  8  0  0  0  0  8  0  0  8  8  8  0  8  0  8  0  0  8  8  0  0  8  8  0  0  8  8  0  0  0  8  0  0  0  0

generates a code of length 52 over Z16 who´s minimum homogenous weight is 40.

Homogenous weight enumerator: w(x)=1x^0+86x^40+12x^41+34x^42+80x^43+311x^44+448x^45+314x^46+1388x^47+2224x^48+5480x^49+6564x^50+11024x^51+9633x^52+11024x^53+6564x^54+5480x^55+2212x^56+1388x^57+314x^58+448x^59+275x^60+80x^61+34x^62+12x^63+79x^64+19x^68+6x^72+2x^76

The gray image is a code over GF(2) with n=416, k=16 and d=160.
This code was found by Heurico 1.16 in 35.3 seconds.