What's the best software to backup a bricked iPhone?

I am an unfortunate iPhone 6 user that would like to somehow save the data on his phone.

I am able to run the phone into "recovery mode" so perhaps not all hope is lost.

I came across a number of applications that say they're capable of doing this, but do you recommend any particular?

Perhaps there exists a free app that can do just this: backup/copy files and data from recovery mode iphone?