The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+58x^44+142x^45+344x^46+654x^47+1333x^48+2000x^49+2300x^50+2678x^51+2553x^52+1966x^53+1199x^54+578x^55+324x^56+126x^57+44x^58+18x^59+16x^60+20x^61+12x^62+8x^63+2x^64+2x^65+4x^66+1x^68+1x^70

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 2.71 seconds.