The generator matrix

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

generates a code of length 48 over Z16 who´s minimum homogenous weight is 42.

Homogenous weight enumerator: w(x)=1x^0+43x^42+112x^43+515x^44+524x^45+1058x^46+1156x^47+1456x^48+1160x^49+1042x^50+520x^51+360x^52+108x^53+92x^54+4x^55+22x^56+3x^58+13x^60+2x^62+1x^64

The gray image is a code over GF(2) with n=384, k=13 and d=168.
This code was found by Heurico 1.16 in 0.747 seconds.