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

generates a code of length 53 over Z16 who´s minimum homogenous weight is 48.

Homogenous weight enumerator: w(x)=1x^0+132x^48+32x^49+64x^50+128x^51+86x^52+1216x^53+64x^54+128x^55+88x^56+32x^57+56x^60+18x^64+2x^68+1x^96

The gray image is a code over GF(2) with n=424, k=11 and d=192.
This code was found by Heurico 1.16 in 0.27 seconds.