The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+292x^44+884x^45+1499x^46+2134x^47+2332x^48+2334x^49+2366x^50+2006x^51+1352x^52+666x^53+295x^54+124x^55+33x^56+34x^57+16x^58+6x^59+6x^60+2x^61+2x^63

The gray image is a code over GF(2) with n=392, k=14 and d=176.
This code was found by Heurico 1.16 in 2.02 seconds.