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

generates a code of length 57 over Z16 who´s minimum homogenous weight is 48.

Homogenous weight enumerator: w(x)=1x^0+48x^48+68x^49+107x^50+174x^51+155x^52+298x^53+466x^54+872x^55+1294x^56+1324x^57+1304x^58+860x^59+428x^60+276x^61+124x^62+108x^63+89x^64+72x^65+37x^66+30x^67+25x^68+10x^69+9x^70+4x^71+8x^72+1x^86

The gray image is a code over GF(2) with n=456, k=13 and d=192.
This code was found by Heurico 1.16 in 1.55 seconds.