The generator matrix

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

generates a code of length 56 over Z16 who´s minimum homogenous weight is 48.

Homogenous weight enumerator: w(x)=1x^0+194x^48+32x^49+406x^50+236x^51+1115x^52+796x^53+2378x^54+1500x^55+3193x^56+1516x^57+2312x^58+772x^59+1080x^60+212x^61+352x^62+52x^63+139x^64+4x^65+50x^66+27x^68+6x^70+9x^72+2x^76

The gray image is a code over GF(2) with n=448, k=14 and d=192.
This code was found by Heurico 1.16 in 5.54 seconds.