The generator matrix

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

generates a code of length 55 over Z16 who´s minimum homogenous weight is 49.

Homogenous weight enumerator: w(x)=1x^0+278x^49+850x^50+1784x^51+2872x^52+3760x^53+4661x^54+4860x^55+4446x^56+3780x^57+2596x^58+1488x^59+742x^60+360x^61+170x^62+52x^63+33x^64+14x^65+10x^66+8x^67+2x^68+1x^70

The gray image is a code over GF(2) with n=440, k=15 and d=196.
This code was found by Heurico 1.16 in 78.3 seconds.