The generator matrix

 1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  2  8  1  2  1  4  1  4  1  1  8  0  1  1  0  1  8  1  2  1  2  4  2  1 12  1  0  1
 0  2  0  2  0  8  2 10  8  2 12 14  0 10  4  6  8  4  2 10  6  2 14  2  6  2  4  2 14  4  0  2 12  6  8  6  2 12 14 10  4  2  2 12  2  2  4  2
 0  0  2  2 12 14  6 12  0  2 10 12  4 14 14  8  0 10 10 12  0 12 14  2 12  6  0  4  8 14  2  4  8  8  2  6  2  2 12 14 14  0  6  4  2 10  2 10
 0  0  0  4  0  0 12  8  4  8 12 12 12  8  4 12  4 12 12  0  0  8 12  8  0  4  4  0  4  0 12 12  8  8  8  0 12  0  8  0  8  4 12  4  4 12  4  0
 0  0  0  0  8  8  8  8  0  0  0  8  8  8  8  0  8  8  8  0  8  0  0  8  8  0  0  0  0  8  0  0  8  8  8  8  8  8  8  8  8  8  0  0  8  0  0  8

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

Homogenous weight enumerator: w(x)=1x^0+122x^42+252x^43+399x^44+730x^45+873x^46+1142x^47+1344x^48+1098x^49+877x^50+556x^51+337x^52+232x^53+94x^54+62x^55+27x^56+18x^57+16x^58+4x^59+4x^60+2x^61+1x^62+1x^66

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 0.95 seconds.