The generator matrix

 1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  2  0  2  8  1  4  1  2  1  1  1 12  0  1 12  1  0  2  1  1  2  1  4  2  2  1  1  1  1  1  2  1  1
 0  2  0  2  0  0 14  6  4  2  4 14 12  6 12  2  0  6  8  2  4  8  6  2  4  2  8 10  8 10  2 12  2 14  2 10  2  2 12  8 14  4  0 10  2 10  6  6  8  4  6  2  0
 0  0  2  2 12  6 14  0  4  6  2 12  0  2 14  4  8  4  2 10  2  2  4 12  0  2  6  6  2 14  0  2  4  8 10  2  0  8 14  6  8  4  2 14 12 12  2 10 14  0  8  2  0
 0  0  0  4  0  0 12  8  8 12  0  0  8  4  0  8  0  0  0  4  8  8  4  0 12  8 12  0 12  8 12  4 12 12 12  0  0  4 12 12 12  8 12  0  0 12  8 12  8  4  8  0  0
 0  0  0  0  8  0  0  0  8  0  0  0  8  8  8  8  0  8  8  8  0  8  8  0  8  0  0  8  8  0  8  8  0  0  0  0  8  0  8  0  8  0  0  0  8  8  0  0  8  8  0  0  0
 0  0  0  0  0  8  0  8  8  8  8  0  0  0  8  0  0  8  0  0  8  8  0  8  8  0  0  8  8  8  0  8  0  8  8  0  8  0  0  8  8  8  8  0  0  8  0  8  8  0  0  8  0
 0  0  0  0  0  0  8  0  0  0  8  8  8  0  0  0  8  8  8  8  0  8  8  0  8  0  8  0  8  8  0  0  8  0  0  8  0  0  8  0  0  8  0  8  8  0  8  0  8  0  0  8  0

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

Homogenous weight enumerator: w(x)=1x^0+76x^44+176x^45+324x^46+522x^47+937x^48+1530x^49+2473x^50+3580x^51+4330x^52+4842x^53+4490x^54+3566x^55+2510x^56+1466x^57+813x^58+478x^59+312x^60+166x^61+82x^62+40x^63+24x^64+12x^65+9x^66+6x^67+2x^68+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 14.9 seconds.