The generator matrix

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

generates a code of length 57 over Z16 who´s minimum homogenous weight is 46.

Homogenous weight enumerator: w(x)=1x^0+50x^46+4x^47+224x^48+76x^49+467x^50+524x^51+911x^52+1904x^53+1824x^54+4568x^55+2732x^56+6280x^57+2713x^58+4648x^59+1758x^60+1904x^61+859x^62+484x^63+427x^64+76x^65+193x^66+12x^67+71x^68+26x^70+16x^72+11x^74+4x^76+1x^78

The gray image is a code over GF(2) with n=456, k=15 and d=184.
This code was found by Heurico 1.16 in 18.3 seconds.