The generator matrix

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

generates a code of length 48 over Z16 who´s minimum homogenous weight is 41.

Homogenous weight enumerator: w(x)=1x^0+46x^41+73x^42+74x^43+120x^44+148x^45+332x^46+762x^47+1052x^48+760x^49+301x^50+148x^51+70x^52+60x^53+52x^54+36x^55+34x^56+10x^57+9x^58+2x^59+2x^60+2x^63+1x^64+1x^82

The gray image is a code over GF(2) with n=384, k=12 and d=164.
This code was found by Heurico 1.16 in 0.522 seconds.