The generator matrix

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

generates a code of length 53 over Z16 who´s minimum homogenous weight is 49.

Homogenous weight enumerator: w(x)=1x^0+148x^49+577x^50+458x^51+806x^52+560x^53+517x^54+304x^55+344x^56+152x^57+148x^58+34x^59+32x^60+5x^62+4x^63+4x^65+1x^66+1x^72

The gray image is a code over GF(2) with n=424, k=12 and d=196.
This code was found by Heurico 1.16 in 0.249 seconds.