After I found the exact sector beginning and end of the NTFS partition with MiniTool Power Wizard, I kept looking for ext4 superblocks after that partition with the following command:
if has to be the drive where you want to search, skip is the current offset from where you start looking. hexdump outputs the bytes. With grep I looked for rows that ended on i30, where i has to be even. "53 ef" is the ext4 superblock.
$ sudoddif=/dev/sdb of=/dev/stdout bs=512skip=1304581count=1000|hexdump-C|grep-e'......30 .. .. .. .. .. .. .. .. 53 ef .. .. .. .. .. ..'
After that I could use mount to try to mount that point:
I used the offset and bytesize and mount it whereever I want.
$ sudo mount -o offset=$((1304581 * 512)) /dev/sda /mnt/whereever
Finally I found the / partition and thus the /home partition. As my /home partition was encrypted I used
to recover my data. The only thing you need for that is the wrapped-passphrase and your passphrase you used to encrypt the home folder.
$ sudo ecryptfs-recover-private
ecryptfs-recover-private will mount the drive as read-only in /tmp/.
As I only want to recover my data and now install a fresh system I will mark this as solved.
Thanks again to YesWeCan for his help!