You usually dont actually need motherboard BIOS updates to get the latest microcode.
If you use linux, you can download the latest microcode bundles from intel's downloadcentre (
https://downloadcenter.intel.com/download/27776/Linux-Processor-Microcode-Data-File?v=t ) and reload the microcode on the fly (not recommended), or preferrably get it loaded extremely early in the boot process. The intel-ucode tools can automate most of it. But more often than not the linux distribution will just push out these updates seamlessly and keep everything updated for you. A quick "dmesg | grep -i microcode" command will let you know what revision is loaded.
Microsoft Windows keeps intel microcode updated via normal software updates also ( eg:
https://support.microsoft.com/en-gb/help/4091664/kb4091664-intel-microcode-updates ).
There are some microcode variants that apparently do need to be loaded pre-OS, my 4970K and 4360T dont, not sure about your 4960X but might be worth checking.
In saying that, shame that ASUS has taken such a poor support route. I have a Gigabte and Asrock here with 9 series chipsets (used on 4th gen CPUs like yours) that didnt have their BIOS's updated in ages until the meltdown/specter debacle, and have received at least two BIOS updates recently to coincide with intel microcode updates.
Of course you always have the more extreme option of using tools to deconstruct your BIOS and update individual modules and reflash it yourself. You could update the Intel ME engine and other stuff while you are at it. Not sure if the risk reward ratio is worth it.