The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+121x^48+6x^56

The gray image is a code over GF(2) with n=384, k=7 and d=192.
This code was found by Heurico 1.16 in 0.0485 seconds.