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

generates a code of length 49 over Z16 who´s minimum homogenous weight is 44.

Homogenous weight enumerator: w(x)=1x^0+148x^44+8x^45+20x^46+256x^47+101x^48+1008x^49+40x^50+256x^51+136x^52+8x^53+4x^54+57x^56+4x^60+1x^88

The gray image is a code over GF(2) with n=392, k=11 and d=176.
This code was found by Heurico 1.16 in 19.6 seconds.