The generator matrix

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

generates a code of length 53 over Z16 who´s minimum homogenous weight is 44.

Homogenous weight enumerator: w(x)=1x^0+36x^44+100x^45+232x^46+378x^47+752x^48+1394x^49+2073x^50+4256x^51+4104x^52+6150x^53+4040x^54+4346x^55+2109x^56+1352x^57+758x^58+342x^59+141x^60+84x^61+51x^62+20x^63+22x^64+6x^65+12x^66+2x^67+3x^68+2x^69+1x^70+1x^74

The gray image is a code over GF(2) with n=424, k=15 and d=176.
This code was found by Heurico 1.16 in 10.6 seconds.