The generator matrix

 1  0  1  1  1 14  1  1  0  1  1  2  6  1  1  1 12  1  1  1  4  1 10  1  1  1  1  1  0  1 14  1  8  2  1 14  1  1  1  2  1  6  1  1  1  6  1  1
 0  1 11 14  5  1  0  3  1  6 13  1  1  4 15  1  1 10  2  9  1 12  1  7  6  3  5  9  1 15  1 10  1 14  8  1 11 13  6 14 14  1  8  2  8  1 11  6
 0  0 12  4  0  4 12  0 12  8 12  4  0  4  8  4  0  8  4  0  4  8  8 12  8  0  0  8  8  0 12  0 12  4  4 12  4  4  8  4 12  0 12  4  4  8 12  0
 0  0  0  8  0  0  0  0  0  0  8  0  0  8  8  0  8  8  8  0  8  8  0  0  0  8  8  0  0  8  8  0  0  8  0  8  0  8  0  0  8  0  0  8  8  8  0  0
 0  0  0  0  8  0  0  0  0  8  0  8  8  8  0  0  0  0  8  8  8  0  8  0  8  0  8  0  0  8  0  8  0  8  0  0  0  8  8  0  8  0  8  0  8  0  8  0
 0  0  0  0  0  8  0  0  0  0  0  0  8  8  0  8  8  8  0  8  0  8  8  8  0  0  0  0  8  8  8  8  8  0  0  0  0  8  0  0  8  8  8  0  0  0  0  8
 0  0  0  0  0  0  8  0  0  0  8  0  0  0  8  0  8  8  8  8  0  0  8  8  8  0  8  0  8  8  0  8  8  0  8  8  8  8  0  0  0  0  0  0  0  0  8  0
 0  0  0  0  0  0  0  8  0  8  0  8  8  8  8  0  0  0  8  0  8  0  8  0  8  8  0  8  0  0  0  8  8  0  8  8  8  0  0  0  0  0  8  8  0  0  0  0
 0  0  0  0  0  0  0  0  8  0  0  8  8  8  0  8  8  8  0  8  8  8  8  0  0  8  8  8  0  0  0  0  8  8  8  8  0  0  0  0  8  8  0  0  8  8  8  8

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

Homogenous weight enumerator: w(x)=1x^0+50x^38+78x^39+151x^40+264x^41+553x^42+1102x^43+2429x^44+4244x^45+8621x^46+8592x^47+13288x^48+8724x^49+8620x^50+4304x^51+2415x^52+1020x^53+532x^54+242x^55+124x^56+84x^57+41x^58+18x^59+19x^60+13x^62+3x^64+2x^66+1x^68+1x^72

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 33.5 seconds.