The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+71x^28+40x^30+371x^32+376x^34+1164x^36+1024x^37+4032x^38+2048x^39+4304x^40+1024x^41+1024x^42+556x^44+152x^46+152x^48+8x^50+32x^52+4x^56+1x^60

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 3.52 seconds.