The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+160x^44+676x^45+1762x^46+2748x^47+5158x^48+7124x^49+9806x^50+10452x^51+10064x^52+7508x^53+4994x^54+2628x^55+1500x^56+556x^57+250x^58+44x^59+64x^60+8x^61+20x^62+13x^64

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 28.8 seconds.