The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+121x^44+428x^45+813x^46+1590x^47+2506x^48+3750x^49+4572x^50+5072x^51+5225x^52+3608x^53+2228x^54+1374x^55+700x^56+430x^57+183x^58+102x^59+20x^60+24x^61+9x^62+4x^63+3x^64+3x^66+2x^67

The gray image is a code over GF(2) with n=408, k=15 and d=176.
This code was found by Heurico 1.16 in 9.33 seconds.