The generator matrix

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

generates a code of length 48 over Z16 who´s minimum homogenous weight is 40.

Homogenous weight enumerator: w(x)=1x^0+120x^40+228x^41+806x^42+1500x^43+2996x^44+4588x^45+7372x^46+9456x^47+11253x^48+9528x^49+7588x^50+4956x^51+2668x^52+1260x^53+704x^54+216x^55+214x^56+12x^57+38x^58+24x^60+4x^62+4x^64

The gray image is a code over GF(2) with n=384, k=16 and d=160.
This code was found by Heurico 1.16 in 33.8 seconds.