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

generates a code of length 48 over Z16 who´s minimum homogenous weight is 36.

Homogenous weight enumerator: w(x)=1x^0+130x^36+344x^40+477x^44+512x^46+13462x^48+512x^50+489x^52+319x^56+119x^60+17x^64+1x^68+1x^88

The gray image is a code over GF(2) with n=384, k=14 and d=144.
This code was found by Heurico 1.16 in 5.67 seconds.