The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+174x^44+460x^45+762x^46+1122x^47+1037x^48+1322x^49+1046x^50+960x^51+563x^52+418x^53+188x^54+42x^55+40x^56+22x^57+19x^58+4x^59+9x^60+2x^61+1x^66

The gray image is a code over GF(2) with n=392, k=13 and d=176.
This code was found by Heurico 1.16 in 0.69 seconds.