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

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

Homogenous weight enumerator: w(x)=1x^0+112x^44+8x^45+114x^46+64x^47+430x^48+624x^49+420x^50+64x^51+99x^52+8x^53+66x^54+24x^56+8x^58+5x^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 0.26 seconds.