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

generates a code of length 48 over Z16 who´s minimum homogenous weight is 39.

Homogenous weight enumerator: w(x)=1x^0+70x^39+129x^40+192x^41+267x^42+372x^43+597x^44+930x^45+1776x^46+2550x^47+2687x^48+2502x^49+1789x^50+1014x^51+560x^52+314x^53+222x^54+136x^55+110x^56+82x^57+39x^58+14x^59+11x^60+12x^61+2x^62+4x^63+1x^66+1x^72

The gray image is a code over GF(2) with n=384, k=14 and d=156.
This code was found by Heurico 1.16 in 9.53 seconds.