The generator matrix

 1  0  1  1  1  4  1 10  1  1  6  1  1  4  1  1  6  1 10  1  1  4  1  1  1  1  1  1  0 10  1  1  2  1  1  4  6  1  1  1  4  6  2  4  1  1  2  1  1  1  0  4  1
 0  1  1  0 11  1 10  1  5  6  1  7 15  1 12  8  1  5  1 10 13  1 10 11  0 13  2  3  1  1  6 14 10  3  1  2  1  8  2 10  1  1 12  0  2  6 12 15 11  5  4  4  0
 0  0  2  6  4  6 10 10  0  0  8  2  2 10  6  0  4  4  2  4  6  8 14  0  4 12 14  6  2  0  6 12  6 12  6  6  6  8 10 14 14  4  6  2  4  8 14  0  0 12 12  0  0
 0  0  0 12  0  4 12  4  0  0  0  8  4  0  0  4 12  4  8 12  4 12  0  4  4  8 12  8  4  8  0  0  8  4 12  4  0  8  8 12 12  4  0 12  4 12  0  8  8  8 12  4  0
 0  0  0  0  8  0  0  0  8  0  0  0  0  0  0  0  0  8  0  0  8  8  8  8  8  8  0  8  8  8  8  8  8  0  0  0  0  8  0  8  8  8  0  0  8  0  8  0  8  8  0  8  0
 0  0  0  0  0  8  0  8  0  0  0  0  0  8  0  0  0  0  8  0  8  0  0  8  8  8  8  0  8  0  8  8  0  8  8  0  0  8  8  0  0  8  8  0  0  8  8  0  8  0  8  8  0
 0  0  0  0  0  0  8  8  8  8  8  8  0  0  0  0  8  0  8  8  0  0  8  0  8  0  0  8  8  8  0  8  0  8  8  0  0  0  0  8  8  8  0  8  8  0  0  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+54x^44+294x^45+458x^46+1112x^47+1824x^48+3096x^49+5189x^50+7002x^51+9265x^52+8948x^53+9624x^54+6704x^55+5096x^56+3240x^57+1782x^58+980x^59+374x^60+278x^61+86x^62+72x^63+21x^64+16x^65+13x^66+2x^67+3x^68+2x^72

The gray image is a code over GF(2) with n=424, k=16 and d=176.
This code was found by Heurico 1.16 in 37.6 seconds.