I am looking for a motherboard, which
- has AM 3+ CPU socket
- support at least 64GB RAM (128GB is better)
- DDR3 memory modules
From 32GB, there is a lot. For 64GB, I found nothing.
As @peterh mentioned, 970 and 990 boards (generally) support 64GB of RAM (ignore the ECS boards that list 128 GB, that's incorrect.) Since these boards aren't widely available anymore (due to their age and relatively limited popularity), a specific recommendation is pretty much useless as it's entirely dependent on what you can find on the relatively-volatile used motherboard market.
However, given the cost of 16 GB DDR3 UDIMMs, you may find it cheaper to just upgrade your entire platform (either to one with DDR4 support or with more RAM slots.) Given the age of the FX platform, you'll probably get a nice performance and feature set bump along the way too.
/proc/cpuinfo
has this:AMD FX(tm)-6300 Six-Core Processor
.