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

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

Homogenous weight enumerator: w(x)=1x^0+147x^28+345x^32+421x^36+1024x^38+12288x^39+1456x^40+408x^44+246x^48+47x^52+1x^76

The gray image is a code over GF(2) with n=312, k=14 and d=112.
This code was found by Heurico 1.16 in 3.93 seconds.