The generator matrix

 1  0  1  1  1  6  1  1  8  1  1 14  1 12  1  1  1 10  4  2  1  1  1  1  0  1  2  1  6  1  4  1  2  1  1  1  6  6 12  0  1  0  1  1  1  1  2  1
 0  1 11  6  5  1  9  8  1  7 14  1  4  1 13 10  3  1  1  1 12 15  2  1  1  4  1  4  1  2  1  2 14  0  2  6  1  1  1  2  0  1  6  6  5 13  8  0
 0  0 12  0  8  0  8  4 12  4 12  4  4  0 12  8  0  8  4  4  0  8  4 12  8 12 12  8  8  4  4  8 12  4 12  0  0  4 12 12  0  0  4  8  0  0  4  0
 0  0  0  8  8  8  0  0  0  8  8  8  8  8  8  0  8  0  8  0  8  0  0  0  0  0  8  0  8  8  0  8  0  8  0  0  0  0  8  8  8  8  0  8  0  8  0  0

generates a code of length 48 over Z16 who´s minimum homogenous weight is 44.

Homogenous weight enumerator: w(x)=1x^0+44x^44+294x^45+286x^46+276x^47+277x^48+344x^49+217x^50+196x^51+48x^52+34x^53+15x^54+8x^55+6x^56+1x^58+1x^70

The gray image is a code over GF(2) with n=384, k=11 and d=176.
This code was found by Heurico 1.16 in 0.102 seconds.