In this example i cut from 00:23:35 to 00:23:39
mkdir frames
# the same quality loose picture, only sound
ffmpeg -i Gran.S02.E11.avi -ss 00:23:35 -t 00:00:04 -acodec copy -vcodec copy cut.avi
# without the same quality
ffmpeg -i Gran.S02.E11.avi -ss 00:23:35 -t 00:00:04 cut.avi
ffmpeg -i cut.avi -vf scale=320:-1:flags=lanczos,fps=10 frames/ffout%03d.png
convert -loop 0 frames/ffout*.png output.gif