The generator matrix

 1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  2  2  2  2  2  1  1  2  1  2  1  1  1  2  2  1  1  2  1  1
 0  8  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  8  8  8  8  0  0  8  8  8  0  8  8  8  0  8  0  8  0  8  8  8  8  0  0  8  8  0  0  0  0  0  0  8  0  0
 0  0  8  0  0  0  0  0  0  0  0  0  8  0  0  8  8  8  8  8  8  0  0  0  0  0  8  8  8  8  8  0  8  0  0  0  8  0  0  8  0  8  8  8  8  8  0  0  0  8  0  0
 0  0  0  8  0  0  0  0  0  0  0  0  8  8  8  8  8  0  8  8  8  0  8  8  8  0  8  0  0  8  8  8  8  8  8  0  0  0  0  0  8  8  0  8  0  8  0  0  8  0  0  0
 0  0  0  0  8  0  0  0  0  0  0  8  0  8  8  0  8  8  8  0  8  8  8  0  0  0  0  0  8  0  0  0  8  0  0  8  8  8  0  0  0  8  8  0  8  0  0  0  8  8  8  8
 0  0  0  0  0  8  0  0  0  0  0  8  0  0  8  8  8  8  8  0  0  8  0  0  8  8  0  0  0  8  8  0  0  0  8  0  8  8  0  0  8  0  0  0  0  8  0  8  8  8  8  8
 0  0  0  0  0  0  8  0  0  0  8  0  0  0  8  8  0  0  8  0  0  8  8  0  8  0  8  0  8  0  8  0  8  8  8  8  8  0  8  8  0  0  0  0  8  8  0  8  0  8  0  0
 0  0  0  0  0  0  0  8  0  0  8  0  0  8  0  0  8  0  0  8  0  8  8  0  0  8  8  8  0  0  8  8  0  8  8  0  8  0  0  0  8  8  8  8  8  8  0  8  8  8  0  0
 0  0  0  0  0  0  0  0  8  0  8  8  8  8  0  0  0  0  8  0  0  0  8  8  8  8  0  0  0  8  0  8  0  0  8  0  8  0  8  8  0  8  0  0  8  8  0  8  0  0  0  0
 0  0  0  0  0  0  0  0  0  8  8  8  8  0  0  8  8  8  8  8  0  8  0  8  0  8  0  8  8  0  0  8  8  8  8  0  8  8  8  8  8  8  8  8  8  0  8  0  8  8  0  0

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

Homogenous weight enumerator: w(x)=1x^0+76x^40+177x^44+42x^46+291x^48+224x^50+6598x^52+196x^54+313x^56+48x^58+131x^60+2x^62+68x^64+21x^68+3x^72+1x^84

The gray image is a code over GF(2) with n=416, k=13 and d=160.
This code was found by Heurico 1.16 in 1.6 seconds.