The generator matrix

 1  0  1  1  1 14  1  1  0  1 14  1  1  6  1  1  1 12  8  1  1  1  1 10  1  1  8  2  1  1  1 14  1  4 12  4  4  2  4  1  6  0  1  2 14  4  0  1
 0  1 11  6  5  1 11  0  1  5  1  6 13  1  8  6  1  1  1  3 10  4 14  1 15  7  1  1  2 10  3  1  6  1  1  1  4  1  1  7  1  1 12  1  1  8  2  0
 0  0 12  0  0  0  0  4  4 12 12  0  8  8  8  4 12  4  0  4  8  4  4 12  0  0  4  0  8  4  8  8  0  0  0 12  8 12 12 12  8  0  0 12  8  0  4  0
 0  0  0 12  0  4  4  4 12 12  8  0  4  8  4  4  0 12  4 12  8  0  0  4  8 12  8  4  4  4  0  4  0 12  0  8 12  8  8  8  8  0  0  8  4  4 12  8
 0  0  0  0  8  0  0  0  0  0  8  0  8  0  0  0  8  8  8  0  8  8  0  0  8  8  8  8  0  0  8  0  0  0  0  8  8  8  0  0  8  8  0  8  0  8  0  8
 0  0  0  0  0  8  0  0  0  8  0  0  8  0  0  8  8  8  8  0  8  0  8  8  0  0  0  8  8  0  8  8  0  0  8  8  0  0  0  8  8  8  8  0  0  0  0  0
 0  0  0  0  0  0  8  0  8  0  0  8  0  8  8  0  0  8  8  0  8  0  8  8  0  8  8  8  0  8  8  8  0  0  8  0  8  8  8  8  0  0  8  0  8  8  0  0
 0  0  0  0  0  0  0  8  0  0  0  8  0  8  8  8  8  8  0  0  0  8  8  0  8  0  0  8  0  8  8  0  8  8  0  8  8  8  0  8  8  0  8  8  8  0  8  0

generates a code of length 48 over Z16 who´s minimum homogenous weight is 38.

Homogenous weight enumerator: w(x)=1x^0+23x^38+94x^39+166x^40+422x^41+474x^42+1606x^43+2188x^44+5344x^45+7328x^46+9974x^47+10533x^48+9932x^49+7035x^50+5316x^51+2340x^52+1624x^53+441x^54+394x^55+114x^56+78x^57+50x^58+22x^59+14x^60+8x^61+8x^62+2x^63+2x^64+1x^66+2x^68

The gray image is a code over GF(2) with n=384, k=16 and d=152.
This code was found by Heurico 1.16 in 34.2 seconds.