The generator matrix

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

generates a code of length 52 over Z16 who´s minimum homogenous weight is 47.

Homogenous weight enumerator: w(x)=1x^0+316x^47+959x^48+1634x^49+1877x^50+2356x^51+2354x^52+2572x^53+1641x^54+1242x^55+802x^56+358x^57+137x^58+76x^59+26x^60+12x^61+7x^62+10x^63+2x^64+2x^66

The gray image is a code over GF(2) with n=416, k=14 and d=188.
This code was found by Heurico 1.16 in 2.17 seconds.