The generator matrix

 1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  2  2  2  1  2  4  2  1  4  1  4  2  8  2  1  1  0  1  4  1  4  2  1
 0 12  0  0  0  4 12  4  0  8  4 12  0  8 12  0  4  8  4 12 12  0  4  0  4  4  4 12  8  8 12 12  0  4  8  4  4  0  0  4  4  0  0  8 12  0  0  0
 0  0 12  0  4  4 12  0  0  0  4  8  4  4  0  8  4 12  0  8 12  8 12  4  0  0 12  0  0  4 12  4  8  4 12  0 12  4  8  8  4  4  4  0  8  0  4  0
 0  0  0 12  4  0 12  4  0  4 12  8 12  0  4  8  0 12 12  0  8 12 12 12  4 12  8  8 12  0  4 12  8  8 12 12  8  4  4  8  8  8 12  4  0 12  4  0
 0  0  0  0  8  0  0  0  8  0  8  8  0  0  0  0  0  8  8  0  8  0  8  8  8  0  0  8  8  0  0  8  0  8  8  8  8  0  8  0  8  0  0  0  0  8  8  0
 0  0  0  0  0  8  0  0  8  8  8  0  8  0  8  8  8  0  8  0  8  0  0  0  0  8  8  0  0  0  8  8  8  8  8  0  8  8  0  0  0  0  0  0  8  8  8  0
 0  0  0  0  0  0  8  0  0  0  0  0  0  8  8  8  8  0  8  0  8  0  8  8  0  0  0  8  8  0  8  8  8  0  0  0  8  0  8  8  0  0  8  8  8  8  0  0
 0  0  0  0  0  0  0  8  8  8  0  8  0  0  0  0  8  8  0  8  0  8  0  0  8  8  8  0  0  0  0  8  8  8  8  8  8  0  8  8  8  8  0  8  8  0  0  8

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

Homogenous weight enumerator: w(x)=1x^0+31x^38+58x^39+143x^40+170x^41+264x^42+470x^43+589x^44+1078x^45+1753x^46+2344x^47+2649x^48+2344x^49+1761x^50+1040x^51+598x^52+432x^53+226x^54+174x^55+93x^56+62x^57+54x^58+10x^59+21x^60+10x^61+5x^62+2x^64+1x^66+1x^70

The gray image is a code over GF(2) with n=384, k=14 and d=152.
This code was found by Heurico 1.16 in 4.87 seconds.