The generator matrix

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

generates a code of length 52 over Z16 who´s minimum homogenous weight is 46.

Homogenous weight enumerator: w(x)=1x^0+122x^46+360x^47+935x^48+1232x^49+1943x^50+2308x^51+2797x^52+2286x^53+1899x^54+1096x^55+812x^56+302x^57+148x^58+76x^59+22x^60+18x^61+12x^62+8x^64+2x^65+1x^66+1x^68+3x^70

The gray image is a code over GF(2) with n=416, k=14 and d=184.
This code was found by Heurico 1.16 in 2.65 seconds.