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

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

Homogenous weight enumerator: w(x)=1x^0+81x^36+154x^40+32x^42+318x^44+224x^46+6597x^48+224x^50+298x^52+32x^54+138x^56+70x^60+21x^64+1x^68+1x^80

The gray image is a code over GF(2) with n=384, k=13 and d=144.
This code was found by Heurico 1.16 in 1.41 seconds.