@romanholiday, Hi, welcome to the forum!
Please read How to get the best out of this forum, if you haven't done yet.
This question isn't easy to answer. We would first need to know if you use a secure connection (https). And if so, what encryption method your server uses.
It might be an encryption not supported by the ESP8266, or your server being too slow.
What number of bytes did you get? Always about the same number? This might help.
Can you see the picture with a browser? Can you download it with a browser?
Jean-Marc