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  2  0  8  1  1  4  1  2  1  1  2  1  0  1  1  2  2  2  8  1  1  1  2  2 12  2  1  1  1  1
 0  2  0  2  0  0  6 14  4  4 10  6 12  6 10 12  4 10  4  4 14  4  6  6 10  4  8  2  2 14  2  4 10  4 12  4 10  2  0  2  2  8  2  2  0 12  0 10 14  2 14  4  8  6  6
 0  0  2  2 12  6  6  4  4  2  6  0  8 10  4 10  4  2  6 14 10  8 14 12  6  2  2  4 12  0 10  6  0 10  0 14  4 14  4 12 12  2 10 14  6 14  8 14 14  0 12  8  4 12 14
 0  0  0  8  0  0  8  0  0  0  8  8  8  0  8  0  8  0  8  8  0  0  0  8  8  0  8  0  8  0  8  8  0  8  8  0  0  0  0  8  8  0  8  8  8  0  8  8  0  8  8  8  8  0  8
 0  0  0  0  8  0  8  0  8  8  0  0  0  8  0  8  8  0  0  0  8  0  0  8  8  8  0  0  8  8  0  8  8  8  0  0  8  8  0  8  0  8  0  8  0  0  8  8  8  8  0  8  0  0  8
 0  0  0  0  0  8  0  8  8  0  8  0  0  8  8  8  0  0  8  0  0  8  8  8  8  8  0  0  0  8  8  8  0  0  8  8  0  0  8  8  0  0  0  0  0  0  8  8  0  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+126x^49+286x^50+360x^51+951x^52+592x^53+1542x^54+762x^55+1498x^56+556x^57+760x^58+236x^59+196x^60+114x^61+94x^62+42x^63+40x^64+18x^65+6x^66+8x^67+1x^68+2x^69+1x^80

The gray image is a code over GF(2) with n=440, k=13 and d=196.
This code was found by Heurico 1.16 in 6.69 seconds.