The generator matrix

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

generates a code of length 38 over Z16 who´s minimum homogenous weight is 28.

Homogenous weight enumerator: w(x)=1x^0+104x^28+56x^30+417x^32+704x^34+3825x^36+6160x^38+3863x^40+704x^42+386x^44+56x^46+84x^48+21x^52+3x^56

The gray image is a code over GF(2) with n=304, k=14 and d=112.
This code was found by Heurico 1.16 in 3.59 seconds.