The generator matrix

 1  0  1  1  1  6  1  1 12  1  1 10  1  1  0  6  1  1  1 12  1 10  1  1  1  1  0  1 12  1  6 12  1  1  1 10  0  1  1  0  1  1  1  0  0  6  1  1
 0  1  3  6  5  1 12  7  1 10  9  1  0  3  1  1  6  5 12  1 10  1 15  9  0  6  1  3  1  5  1  1 12  9 10  1  1  5  0  1  3  5  6  1  1  1  0  0
 0  0  8  0  0  0  0  0  0  0  0  0  0  8  8  8  0  0  8  8  8  8  0  0  0  0  0  0  0  0  8  8  8  8  0  8  0  8  8  8  8  8  0  8  8  0  0  0
 0  0  0  8  0  0  0  0  0  0  0  0  0  0  0  0  8  8  8  0  8  0  8  8  0  8  0  8  0  8  8  0  0  8  0  0  0  8  8  8  0  8  8  8  8  8  0  0
 0  0  0  0  8  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  8  0  8  8  8  8  8  8  0  8  8  8  8  0  8  8  8  8  8  8  8  0  0  8  0  0
 0  0  0  0  0  8  0  0  0  0  0  8  0  0  8  8  0  8  0  0  0  0  8  8  8  0  0  0  8  8  8  0  8  0  8  8  8  0  0  8  8  0  8  0  0  0  0  0
 0  0  0  0  0  0  8  0  0  0  0  8  8  0  0  8  8  0  0  8  8  8  8  0  0  8  8  0  8  0  8  0  0  8  8  0  8  8  8  8  8  0  0  8  8  0  0  0
 0  0  0  0  0  0  0  8  0  0  8  0  0  0  8  8  0  8  8  8  8  8  0  8  8  8  0  8  0  8  0  8  0  0  0  0  8  0  8  0  8  8  0  8  8  8  0  0
 0  0  0  0  0  0  0  0  8  0  8  8  0  8  8  0  8  8  0  8  8  0  0  8  0  0  8  0  0  8  0  8  0  0  0  0  0  8  8  8  0  0  0  8  0  8  0  0
 0  0  0  0  0  0  0  0  0  8  8  8  8  8  0  8  0  0  8  0  8  0  0  8  8  0  8  8  8  0  8  8  0  0  0  8  8  0  8  0  0  8  0  0  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+71x^36+36x^38+24x^39+288x^40+216x^41+612x^42+992x^43+2763x^44+4704x^45+7288x^46+10448x^47+10678x^48+10448x^49+7288x^50+4704x^51+2753x^52+992x^53+612x^54+216x^55+246x^56+24x^57+36x^58+73x^60+17x^64+4x^68+2x^72

The gray image is a code over GF(2) with n=384, k=16 and d=144.
This code was found by Heurico 1.16 in 30.6 seconds.