The generator matrix

 1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  2  1  1  1  2  2  1  1  4  1  2  1  1  1  1  0  1  1  1  1  1  4  0  2  4  1  1  1  1  1  1
 0 12  0 12  0 12  0 12  0  4  8  0 12 12  4  0  8 12  0  8  0 12 12  0  0 12  8 12 12 12  8 12  4  4  8  4 12  4 12  4 12 12  0  0 12  4  0  0
 0  0  8  0  0  0  0  0  0  0  8  8  0  8  8  0  8  0  8  8  0  0  0  8  8  0  8  0  8  0  8  8  8  0  8  0  0  0  8  0  0  8  8  0  8  0  0  0
 0  0  0  8  0  0  0  0  0  8  0  0  0  8  8  0  0  0  8  8  8  0  8  8  0  8  0  8  0  8  8  8  8  8  8  8  0  0  8  0  0  8  0  8  8  8  0  8
 0  0  0  0  8  0  0  0  0  0  0  8  0  0  0  8  0  0  0  8  8  8  8  8  8  0  0  8  8  0  0  8  8  0  0  8  8  8  8  0  0  8  8  8  8  0  8  8
 0  0  0  0  0  8  0  0  0  0  0  0  8  8  8  0  0  0  0  0  0  8  8  8  8  0  8  8  0  0  8  8  0  8  8  8  0  8  0  8  8  0  8  8  8  8  8  0
 0  0  0  0  0  0  8  0  0  0  0  8  0  0  0  8  8  8  8  8  8  0  0  0  0  8  8  0  8  8  0  0  0  8  0  0  8  8  8  0  8  0  0  8  0  8  8  0
 0  0  0  0  0  0  0  8  0  8  0  0  8  8  0  8  8  8  0  0  8  0  8  0  8  0  8  8  0  8  8  0  8  8  0  0  0  8  8  8  0  0  0  8  0  0  0  0
 0  0  0  0  0  0  0  0  8  0  8  8  8  0  8  8  8  8  0  0  0  8  0  0  8  8  0  8  0  0  8  0  0  0  8  0  8  8  8  0  8  0  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+23x^38+18x^39+56x^40+74x^41+92x^42+192x^43+126x^44+720x^45+664x^46+1556x^47+1187x^48+1556x^49+652x^50+720x^51+110x^52+192x^53+72x^54+74x^55+34x^56+18x^57+24x^58+19x^60+8x^62+2x^64+1x^70+1x^76

The gray image is a code over GF(2) with n=384, k=13 and d=152.
This code was found by Heurico 1.16 in 1.3 seconds.