The generator matrix

 1  0  1  1  1  6  1  1 12  1  1 10  1  1  0  6  1  1 12  1 10  1  1  1  1  1  0  1 12  1  6  6  1  1  1  0  4  1  1
 0  1  3  6  5  1 12  7  1 10  9  1  0  3  1  1  5 15  1  9  1  6 12 10  3  5  1  0  1  6  1  1  0  3  3  1  0  0  0
 0  0  8  0  0  0  0  0  0  0  0  0  0  0  8  8  8  8  8  8  8  0  0  0  0  0  0  0  8  8  8  0  0  0  8  8  8  0  0
 0  0  0  8  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  8  0  8  8  8  8  8  8  8  8  8  8  0  8  0  0  8
 0  0  0  0  8  0  0  0  0  0  0  0  0  8  8  8  8  0  8  8  8  8  8  8  8  0  8  0  0  8  8  8  8  8  0  8  8  8  8
 0  0  0  0  0  8  0  0  0  0  0  8  0  0  0  0  0  0  8  0  8  8  8  8  0  8  8  8  0  0  0  8  8  0  0  0  8  8  0
 0  0  0  0  0  0  8  0  0  0  0  8  8  8  0  0  8  8  8  8  0  0  8  0  0  8  0  0  8  8  0  8  0  8  8  0  0  0  8
 0  0  0  0  0  0  0  8  0  0  8  0  0  0  0  0  8  0  0  8  0  8  8  8  0  8  0  8  0  8  0  8  0  8  8  8  8  8  8
 0  0  0  0  0  0  0  0  8  0  8  8  0  8  0  8  0  8  0  8  8  8  0  8  8  8  8  8  0  8  8  8  0  0  0  0  0  0  0
 0  0  0  0  0  0  0  0  0  8  8  8  8  0  8  8  0  0  8  8  0  0  8  8  8  8  0  0  0  8  0  0  0  0  8  0  8  8  8

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

Homogenous weight enumerator: w(x)=1x^0+36x^28+4x^29+70x^30+64x^31+249x^32+344x^33+767x^34+1856x^35+4299x^36+8344x^37+9965x^38+13568x^39+9909x^40+8384x^41+4302x^42+1856x^43+794x^44+324x^45+210x^46+64x^47+64x^48+8x^49+35x^50+7x^52+9x^54+1x^56+2x^62

The gray image is a code over GF(2) with n=312, k=16 and d=112.
This code was found by Heurico 1.16 in 21.4 seconds.