The generator matrix

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

generates a code of length 48 over Z16 who´s minimum homogenous weight is 36.

Homogenous weight enumerator: w(x)=1x^0+69x^36+40x^38+4x^39+302x^40+36x^41+248x^42+144x^43+680x^44+336x^45+3040x^46+504x^47+5608x^48+504x^49+3040x^50+336x^51+668x^52+144x^53+248x^54+36x^55+246x^56+4x^57+40x^58+84x^60+19x^64+3x^68

The gray image is a code over GF(2) with n=384, k=14 and d=144.
This code was found by Heurico 1.16 in 4.96 seconds.