Backing up from within recovery mode?
So my MacBook pro has gone into this weird mode. I'm not sure but I think it's the safe mode (grey Apple logo, a circling 'loading' thing and a progress bar). After the bar loads fully, the laptop just shuts down itself. So after a few tries, I googled on my phone and on many forums, they said to press the option key to go into recovery mode. Now, I wanna back up my files into an external hard drive. I have one with more than 400 gb free.
And I followed the instructions for backing up in recovery mode: go into disk utility, choose the Mac hard drive and choose make new image with destination as the external hard drive. The Mac hard drive is just about 170 something gb, more than enough space available on the external hard drive but every time I try making a new image, it says 'Unable to create "Macintosh HD.dmg" (file too large)'. I really don't understand what to do. I have my English assignment in there and my deadlines already over, I'm desperate (it's a 3000+ word essay and I don't have the time to write it all again). Please help!
My laptop is a MacBook pro 13" mid 2012 model. I will seriously be really grateful for any help, at all.