The generator matrix

 1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1 12  2  2  0  1  0  1  2  8  1  1  1  1  1  8  1  2  2 12  4  2  1  2  1  1  2  1 12  1  1  4  2  4  1
 0  2  0  2  0  0  6  6  4  4 10  6 12  4 14 14  4 14  2  2 12  4 14  2 10 14  2  0  0 12  8  2  8  6  8  0  8  2  2 10  2  0  2  6  4 10  4  6  8  8  2 12  2  2  8  2  8
 0  0  2  2 12  6  6  0 12  2 14 12  0  6  6  4 12  2  4  4 14  8  2 14  6  4  8  2  2  0  2  4  6  6  0  6  4  2  8  6 10  2 12  0  0  8  8  8 14  6 14 10  6 14  2 12  4
 0  0  0  8  0  0  0  0  8  0  0  8  8  0  8  8  8  8  8  0  8  0  0  8  0  0  8  0  8  8  0  0  8  8  0  8  0  8  0  8  0  0  8  0  0  8  8  8  8  8  8  8  0  8  8  0  8
 0  0  0  0  8  0  0  8  0  8  8  0  0  8  8  8  8  0  8  0  0  0  8  0  0  0  8  0  8  8  0  8  0  0  0  8  8  8  8  0  0  8  0  0  8  8  8  0  0  0  8  8  0  8  8  0  8
 0  0  0  0  0  8  0  0  0  8  8  8  8  0  8  8  0  8  0  8  0  8  8  0  0  0  0  8  0  0  0  8  0  8  0  8  8  8  0  0  0  8  8  8  0  8  8  0  0  8  0  8  8  8  0  8  0
 0  0  0  0  0  0  8  0  8  0  8  8  8  0  0  8  8  0  0  8  0  8  0  8  8  8  8  8  0  0  0  0  8  8  8  8  8  0  8  0  0  0  8  8  8  8  0  8  8  8  0  0  0  0  0  8  0

generates a code of length 57 over Z16 who´s minimum homogenous weight is 49.

Homogenous weight enumerator: w(x)=1x^0+32x^49+196x^50+316x^51+559x^52+884x^53+1190x^54+2052x^55+1709x^56+2740x^57+1704x^58+1932x^59+1082x^60+892x^61+439x^62+300x^63+195x^64+60x^65+50x^66+8x^67+29x^68+2x^70+7x^72+2x^74+2x^76+1x^78

The gray image is a code over GF(2) with n=456, k=14 and d=196.
This code was found by Heurico 1.16 in 4.4 seconds.