I’ve used the Tieline feature before, actually in the opposite direction to you, but if you put timecode into, say, input 16 of the DX168, you could route that via Tieline to come out an output XLR on the back panel, then maybe convert it to midi there to feed whatever.
I would have thought a Midi input on the stage box won’t happen as it would require new hardware, but this would work fine. Obviously you lose a physical input on the DX, and you could just put it into a channel and take a direct output to an XLR output too. Obviously, whichever way you patch it, it has to be part of every Preset, or isolated from recall.