The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+142x^48+92x^50+16x^51+329x^52+96x^53+648x^54+752x^55+1391x^56+1344x^57+1296x^58+752x^59+739x^60+96x^61+216x^62+16x^63+147x^64+52x^66+47x^68+12x^72+5x^76+2x^80+1x^88

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 2.06 seconds.