DS-77xx also do not support 4K according to specs, they are supposed to wotk with the following resolutions, like DS-76xx:
Recording Resolution: 6MP/5MP/3MP/1080P/UXGA/720P/VGA/4CIF/DCIF/2CIF/CIF/QCIF
But you bet it does work at 4K! So I would not say that 76xx does not support it, until someone tries it with a new firmware.