The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+140x^44+328x^45+874x^46+1552x^47+2617x^48+3892x^49+4608x^50+4996x^51+4676x^52+3700x^53+2466x^54+1512x^55+752x^56+364x^57+160x^58+36x^59+60x^60+4x^61+16x^62+10x^64+4x^66

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 9.79 seconds.