The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+28x^46+44x^47+127x^48+176x^49+427x^50+694x^51+1741x^52+2660x^53+5668x^54+6488x^55+10400x^56+8608x^57+10506x^58+6396x^59+5785x^60+2728x^61+1643x^62+652x^63+323x^64+144x^65+135x^66+62x^67+39x^68+20x^69+18x^70+12x^72+4x^74+3x^76+3x^78+1x^80

The gray image is a code over GF(2) with n=456, k=16 and d=184.
This code was found by Heurico 1.16 in 42.4 seconds.