Few months ago I was desperate for a tool that recorded the terminal and allowed me to save the animation as a GIF. While asciinema (at least at that time) didn’t have any straightforward way to do this, I looked elsewhere and found https://gifox.io and must admit have been very impressed with it.
On Linux, there is also peek[1], and on Windows, there is ScreenToGif[2]. Both are open source.
Another option is to use screencasting software like OBS Studio[3] (and for Linux, I highly recommend SimpleScreenRecorder[4]) to get a high-quality video capture, then throwing it through gifski[5] to get really high quality GIFs.
Especially if you plan on uploading to a gif-site you might as well just capture video and upload that - they tend to do gif-conversion themselves these days.
[0] https://www.cockos.com/licecap/
[1] https://github.com/phw/peek
[2] http://www.screentogif.com/
[4] http://www.maartenbaert.be/simplescreenrecorder/
[5] https://gif.ski/