The generator matrix

 1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  2  0  8  2  1  2  1  1  2  2  1  8  1  1  4  1  1  1  1  2  1  4  4  1  1  0  1  2  1  1  2  1
 0  2  0  6  0  6  0  2  4  6 12 10 12  2  4 14  6  2  2  6 12 14 14  0  2 10 10  2  6 12  2 10 14 14  0  6  4  2 12  0  4  4 12  2  0 14 14  0
 0  0 12  0  0  4  4  4  4  0  8  4 12  8  0  4  4  8 12  8  0  8  8  0  4  8  0  0  8  4 12 12  0  0  8  8 12  4  4  0  4  4  0  8 12  0  0  0
 0  0  0 12 12  4  4  0  8  8  8  4 12 12  4  8 12  8  8  8  0 12 12  8  8  0  8 12  0  4  8  4  4  4  8  0 12  0 12 12  8  4 12 12  4  8  4  0
 0  0  0  0  8  0  0  0  8  8  8  0  8  0  0  0  8  8  0  8  8  0  8  8  0  0  0  0  8  0  8  0  8  0  8  8  0  0  0  8  8  8  0  0  0  0  0  0
 0  0  0  0  0  8  0  0  0  0  8  0  8  0  0  8  8  0  0  0  0  8  8  8  8  0  0  8  0  8  0  0  8  0  8  8  8  0  0  0  8  8  8  8  0  8  0  0
 0  0  0  0  0  0  8  0  0  8  0  8  0  8  8  0  0  0  8  8  8  0  0  0  0  8  8  8  0  8  0  8  8  0  8  0  0  8  8  8  0  0  0  0  8  8  0  0
 0  0  0  0  0  0  0  8  8  8  8  8  0  8  0  0  8  8  8  0  8  8  0  0  8  8  0  8  8  8  0  0  8  8  8  0  8  0  8  8  0  8  8  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+44x^38+60x^39+213x^40+292x^41+556x^42+652x^43+1592x^44+1836x^45+4724x^46+3318x^47+6283x^48+3290x^49+4630x^50+1846x^51+1696x^52+666x^53+472x^54+246x^55+171x^56+58x^57+60x^58+22x^59+24x^60+2x^61+8x^62+4x^64+2x^66

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.