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  1  1  1  1  1  1  1  1  1  1  1  1  1  2  4  1  1  1  0  2  4  2  1  1  4  4  4  4  0  0  2  2  2  1
 0 12  0  0  0  0  0  0  0 12 12  4  4  4  4  4  0 12  4  8  0  8  0  4  8  4  0 12  0  8  8  0 12  4  4  8 12  0  0  0  4  8  8 12  4  4  8 12  8  8 12  8  0  8  4  4 12
 0  0 12  0  0  0  4 12  4  4 12  8  4  8  8  4  0  4 12 12  4  8  8 12  8  0 12  0  0 12 12 12 12 12  0 12 12 12  8  0  0  4  8  4  4 12  0  8  4 12  8  8  8  0  4 12  0
 0  0  0 12  0  4  4 12  0  8 12 12 12 12  8  0 12  0  4  0  0  4  8 12  4  8 12 12  8  4 12  0 12  8  0  8  0 12  8  4  8 12 12 12 12  8  4  0  4  0 12  8  0  0  4  4  4
 0  0  0  0 12  4  0 12  4 12  8  4 12  8 12  0  4  4  0 12  0  0  8 12  0 12  4  8  4  0  8  4  0  8  8  8 12  4  4 12  4  4  0  0  4 12  4  0  4  4 12  4  4  4  4  4  4
 0  0  0  0  0  8  0  0  8  8  0  8  0  0  8  8  0  0  0  0  8  8  0  8  0  8  0  8  0  0  8  8  8  0  0  8  8  8  8  0  8  0  8  0  8  0  0  0  0  8  0  8  0  8  0  8  0
 0  0  0  0  0  0  8  0  8  8  8  0  0  0  8  8  0  8  0  0  0  0  8  8  8  0  8  0  8  8  0  8  8  8  8  0  0  8  8  8  0  0  0  8  0  0  0  8  8  0  8  8  8  8  0  8  8
 0  0  0  0  0  0  0  8  0  0  0  0  8  0  0  8  8  8  0  8  8  8  0  0  0  0  8  8  0  8  0  8  0  8  8  0  8  8  8  0  8  0  0  8  8  0  0  8  0  0  8  8  8  0  8  8  0

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

Homogenous weight enumerator: w(x)=1x^0+102x^46+422x^48+20x^49+765x^50+148x^51+1246x^52+908x^53+2881x^54+2916x^55+4893x^56+4292x^57+4771x^58+2940x^59+2884x^60+900x^61+1331x^62+140x^63+649x^64+24x^65+321x^66+133x^68+61x^70+11x^72+7x^74+1x^78+1x^84

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 23 seconds.