The generator matrix

 1  0  0  1  1  1  2  2  1 14  1  4  1  1  1  1  1  6  4  2  1  1  6  0 12  1  1  1 10 14  1 12  0  1  1  6  6  1  6 14  1 10  4  4  1  1  6  1  0
 0  1  0  0  5 13  1  4  7  1  6  1 10 11  5 15 10  1 14  1  6  0  4  1  1 15  8  5  1  8  6  1  4  4 14  1  1  5 10  1  0  1  1  1  9 10  1  0  1
 0  0  1  3  3  4  7  1  7  2  3  7 14  2 15 12  0  8  1 13  9  5  1 10  1  5 14  2 11  1  5  0  1 11 14 12  2  8  1  9  7  9  7 12  5 10  8  0  3
 0  0  0  8  0  0  8  8  8  8  0  0  8  8  0  8  8  8  0  8  8  0  0  0  8  8  0  8  0  8  8  0  8  0  8  0  8  8  0  0  0  0  8  8  8  0  0  8  8
 0  0  0  0  8  0  0  0  0  0  0  0  0  0  0  8  8  8  8  8  0  8  8  0  8  0  0  0  8  8  8  8  8  0  8  8  8  0  0  8  8  0  8  0  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+266x^44+828x^45+1532x^46+2216x^47+2397x^48+2296x^49+2372x^50+2004x^51+1187x^52+732x^53+340x^54+80x^55+77x^56+16x^57+12x^58+20x^59+7x^60+1x^64

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 1.85 seconds.