ffmpeg can output high quality GIF

 ffmpeg -ss 30 -t 3 -i input.mp4 \
    -vf "fps=10,scale=320:-1:flags=lanczos,split[s0][s1];[s0]palettegen[p];[s1][p]paletteuse" \
    -loop 0 output.gif 

• This example will skip the first 30 seconds (-ss 30) of the input and create a 3 second output (-t 3).
• fps filter sets the frame rate. A rate of 10 frames per second is used in the example.
• scale filter will resize the output to 320 pixels wide and automatically determine the height while preserving the aspect ratio. The lanczos scaling algorithm is used in this example.
• palettegen and paletteuse filters will generate and use a custom palette generated from your input. These filters have many options, so refer to the links for a list of all available options and values. Also see the Advanced options section below.
• split filter will allow everything to be done in one command and avoids having to create a temporary PNG file of the palette.
• Control looping with -loop output option but the values are confusing. A value of 0 is infinite looping, -1 is no looping, and 1 will loop once meaning it will play twice. So a value of 10 will cause the GIF to play 11 times.