The generator matrix

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

generates a code of length 51 over Z16 who´s minimum homogenous weight is 46.

Homogenous weight enumerator: w(x)=1x^0+258x^46+1000x^47+1414x^48+2196x^49+2254x^50+2772x^51+2022x^52+1756x^53+1208x^54+928x^55+333x^56+140x^57+38x^58+36x^59+12x^60+4x^61+6x^62+2x^64+4x^66

The gray image is a code over GF(2) with n=408, k=14 and d=184.
This code was found by Heurico 1.16 in 2.11 seconds.