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

generates a code of length 39 over Z16 who´s minimum homogenous weight is 28.

Homogenous weight enumerator: w(x)=1x^0+70x^28+189x^32+48x^34+364x^36+304x^38+6144x^39+533x^40+144x^42+230x^44+16x^46+105x^48+40x^52+3x^56+1x^64

The gray image is a code over GF(2) with n=312, k=13 and d=112.
This code was found by Heurico 1.16 in 0.974 seconds.