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  2  1  2  1  1  2  1  1  2  1  1  1  1  1  2  2  1  1  2  4  1  2  1  2
 0  8  0  0  0  0  0  0  0  0  0  8  0  0  8  8  0  0  0  0  8  8  8  8  0  8  0  8  0  0  8  0  8  8  8  0  8  8  0  0  8  8  0  0  8  8  0  0  8  8  0  0
 0  0  8  0  0  0  0  0  0  0  0  8  8  8  8  8  0  0  0  8  8  0  0  0  0  0  8  8  8  8  0  0  8  0  8  0  0  0  0  8  0  0  0  8  8  8  8  8  8  8  0  0
 0  0  0  8  0  0  0  0  0  0  8  0  8  8  0  8  8  0  8  0  8  8  8  8  0  8  8  8  8  8  0  8  8  0  8  0  8  8  8  0  8  8  8  0  8  0  8  8  0  0  8  8
 0  0  0  0  8  0  0  0  0  0  8  0  0  8  8  8  8  8  0  8  0  0  0  0  0  8  0  8  8  8  8  8  0  0  0  0  8  0  0  0  8  8  0  8  8  8  0  8  8  0  8  8
 0  0  0  0  0  8  0  0  0  8  0  0  0  8  8  0  8  0  8  8  8  0  0  8  0  8  8  8  0  0  8  0  0  8  0  8  0  0  8  8  8  8  8  0  0  8  0  0  0  8  0  0
 0  0  0  0  0  0  8  0  0  8  0  0  8  0  0  8  8  8  0  8  8  0  8  8  0  0  0  8  0  8  8  0  8  0  0  0  8  8  0  8  8  0  8  0  0  8  0  8  0  0  8  0
 0  0  0  0  0  0  0  8  0  8  8  8  8  0  0  0  0  0  8  8  8  8  8  0  8  8  8  0  0  8  8  0  0  8  8  8  8  0  8  0  0  0  8  8  8  8  0  0  0  8  0  8
 0  0  0  0  0  0  0  0  8  8  8  8  0  0  8  8  8  0  0  0  8  0  0  0  8  0  0  8  8  8  0  0  0  8  0  0  8  8  8  8  0  8  0  0  0  8  8  0  0  0  8  8

generates a code of length 52 over Z16 who´s minimum homogenous weight is 44.

Homogenous weight enumerator: w(x)=1x^0+118x^44+20x^46+190x^48+116x^50+512x^51+2256x^52+512x^53+92x^54+125x^56+28x^58+80x^60+35x^64+9x^68+1x^72+1x^84

The gray image is a code over GF(2) with n=416, k=12 and d=176.
This code was found by Heurico 1.16 in 74.8 seconds.