The generator matrix

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

generates a code of length 54 over Z16 who´s minimum homogenous weight is 44.

Homogenous weight enumerator: w(x)=1x^0+46x^44+78x^45+229x^46+386x^47+769x^48+1458x^49+3033x^50+4890x^51+7494x^52+9518x^53+9643x^54+9682x^55+7593x^56+4950x^57+2928x^58+1330x^59+722x^60+348x^61+197x^62+84x^63+67x^64+32x^65+31x^66+12x^67+10x^68+3x^70+1x^72+1x^80

The gray image is a code over GF(2) with n=432, k=16 and d=176.
This code was found by Heurico 1.16 in 41.3 seconds.