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

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

Homogenous weight enumerator: w(x)=1x^0+47x^38+78x^39+107x^40+194x^41+236x^42+326x^43+568x^44+840x^45+1784x^46+2636x^47+2753x^48+2676x^49+1754x^50+876x^51+573x^52+320x^53+215x^54+166x^55+69x^56+58x^57+48x^58+14x^59+18x^60+8x^61+10x^62+6x^64+2x^66+1x^68

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 5.07 seconds.