The generator matrix

 1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  2  1  4  2  2  1  0  2  2 12  1  2  1  1  4  1  4  1  1  1  1  1  1  1  1  8  1  1  1
 0  2  0  0  0  2  6 14  8  8 14  6 12 10  8  6 14 12  6 14  0  0 10 10  2  2 12 12 12  0 12  2  4  8 12  0  2 10  2  6  0 10  6  0  2 10 10  2  2 10  0
 0  0  2  0  2  2 10  0 12 14  8  2 12 12  2 14 10  2 14  0  4  6  6 12  6  6 14 12  2  6  6  6  8 12  2  4  4 14  8  6  6  8  6  4  0  6  0  8 10 10  0
 0  0  0  2  2  8 10  2  4  0 14 12  2  0  6  6  8  8  2  4 14  2  8 14 12  2 12  0 12 14 14 14  8 14 12 10 10 10  0 14  4 10 10  8  4  8  2  2  6  4  0
 0  0  0  0  8  8  0  8  8  8  0  0  8  8  0  8  0  8  8  8  0  0  0  0  8  8  0  8  8  8  0  0  0  0  0  8  8  0  8  0  8  0  0  0  0  8  8  0  8  0  0

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

Homogenous weight enumerator: w(x)=1x^0+141x^44+262x^45+509x^46+750x^47+1222x^48+1626x^49+2610x^50+2494x^51+2369x^52+1620x^53+1186x^54+622x^55+425x^56+212x^57+200x^58+66x^59+34x^60+22x^61+4x^62+4x^63+2x^65+2x^66+1x^78

The gray image is a code over GF(2) with n=408, k=14 and d=176.
This code was found by Heurico 1.16 in 3.58 seconds.