The generator matrix

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

generates a code of length 51 over Z16 who´s minimum homogenous weight is 44.

Homogenous weight enumerator: w(x)=1x^0+143x^44+568x^45+1520x^46+3152x^47+5304x^48+7772x^49+9112x^50+10288x^51+9481x^52+7880x^53+5080x^54+3040x^55+1322x^56+508x^57+204x^58+64x^59+55x^60+8x^61+16x^62+13x^64+4x^66+1x^68

The gray image is a code over GF(2) with n=408, k=16 and d=176.
This code was found by Heurico 1.16 in 29.5 seconds.