The generator matrix

 1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  2  0  1  2  8  2  1  1 12  1  4  1  2  1  1  1  1  1  1  2  2  4  1  1  1  2  2  1  2  2  8  1  1
 0  2  0 14  4  6 12  2  0  6 14 12  8  2 10  6  2  4 14  2  2 14  2  2  8  2  0 10 10  4  6 14  0  4  6 12  4  6 14 10  2 10 14 14  2  4  8  8
 0  0 12  4  4  0  0  4  0  0  4  8  4 12  8  0  0  4  4  4 12 12 12  8 12 12  0  0  8  4  0  4  0 12  0 12 12  8  0  8  4  8  0  4  4 12  4  4
 0  0  0  8  0  0  0  0  0  0  8  0  0  0  0  0  8  0  0  0  8  0  8  8  8  8  0  8  0  0  0  8  8  8  8  0  8  8  8  0  8  8  0  0  8  0  0  0
 0  0  0  0  8  0  0  0  0  8  8  8  8  0  0  0  8  8  0  8  0  0  0  8  8  0  8  0  8  0  0  8  8  0  8  0  0  8  0  0  8  8  8  8  0  0  0  0
 0  0  0  0  0  8  0  0  0  0  0  0  0  0  8  0  0  8  8  8  8  8  8  0  0  8  0  0  0  8  8  8  8  8  8  8  0  8  8  0  0  0  8  8  8  0  0  0
 0  0  0  0  0  0  8  0  0  0  0  8  0  0  0  8  8  0  8  8  8  8  8  0  8  0  8  0  8  8  8  8  0  0  0  0  8  8  8  8  8  8  8  8  0  0  0  0
 0  0  0  0  0  0  0  8  0  0  0  0  0  8  0  0  8  8  0  0  8  8  0  8  8  8  8  8  0  8  8  0  0  8  8  0  8  0  8  8  0  0  8  8  0  8  8  0
 0  0  0  0  0  0  0  0  8  0  0  0  8  8  8  8  8  8  0  8  0  0  8  0  0  0  8  8  0  8  0  0  0  8  0  0  0  8  8  8  8  0  8  0  0  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+67x^38+8x^39+258x^40+172x^41+661x^42+612x^43+1507x^44+2576x^45+2859x^46+5824x^47+3643x^48+5864x^49+2896x^50+2616x^51+1527x^52+592x^53+589x^54+152x^55+196x^56+12x^57+81x^58+4x^59+29x^60+13x^62+6x^64+2x^66+1x^68

The gray image is a code over GF(2) with n=384, k=15 and d=152.
This code was found by Heurico 1.16 in 14.4 seconds.