I was able to fix the sound after I found out that sound worked through headphones.
I used ThinkWiki to find what audio chipset/codec is used on the X200t: Intel HD Audio with a CX20561 codec
I found out that this chipset was supported by FreeBSD.
I found a post by Sirvo who had the same chipset on his R400 and fixed it by adding the following lines to /boot/device.hints
hint.hdac.0.cad0.nid26.config="as=2 seq=0 device=Speaker"
hint.hdac.0.cad0.nid22.config="as=2 seq=15 device=Headphones"