The generator matrix

 1  0  1  1  1  6  1  1 12  1  1 10  1  1  8 14  1  1  2  1  4  1  1  1  8  1  6  1  1  1  1 14  1  1  1  1  0  1 10  1  1  1  2 12  2  2  8  1  4  4  2
 0  1 11  6 13  1 12  7  1 10  5  1  9  8  1  1  3 14  1  1  1  4  2 15  1  5  1  0  3 13  6  1 14  9  8  8  1  1  1  6  9 12  8  1  4  1  1 12  1  1  4
 0  0 12  0  4  0  0  4  8  8  8  0  8  4 12 12  8 12 12  4  4  4  4  8  4  0  0  8  8  4  0  4  4  0 12  4  8  4  0  0  8  8 12  8  4  4  4  0 12  4 12
 0  0  0  8  0  0  0  0  8  0  8  8  8  8  0  0  0  0  8  0  8  8  0  0  8  8  8  0  0  8  0  8  0  8  0  8  0  0  8  8  0  8  0  8  0  0  0  8  0  8  8
 0  0  0  0  8  0  0  8  0  0  0  8  8  8  8  0  8  8  0  8  0  0  8  8  8  0  0  0  8  0  8  8  0  8  0  8  0  0  8  0  8  8  8  0  0  0  8  0  0  0  0
 0  0  0  0  0  8  0  8  0  8  8  0  0  8  0  8  8  0  8  0  8  8  8  0  0  0  8  8  8  0  0  8  0  8  0  8  0  8  0  8  8  0  0  8  0  8  8  0  0  8  8
 0  0  0  0  0  0  8  0  0  8  0  0  0  0  0  8  8  8  8  8  0  8  8  8  0  8  0  0  0  0  8  8  0  0  8  8  8  0  8  0  0  8  8  8  8  0  0  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+93x^44+128x^45+366x^46+636x^47+1369x^48+1904x^49+2378x^50+2844x^51+2258x^52+1952x^53+1239x^54+596x^55+317x^56+112x^57+95x^58+20x^59+44x^60+15x^62+13x^64+3x^66+1x^68

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 2.76 seconds.