The normal MC3810 only does G729 when equiped with the basic codec card.
Look into the DSP card. If the chips have a 542 stenciled on the chips, you got the older DSP ‘s, adn those only handle g729 and g711,among other extrange ones that are not too much help.
In order to get g723 you need a MC3810 with 549 ‘s DSP chips, the one that are normally on the MC3810 V3.
Look at the prices on ebay. That is the reason why the MC3810 with the good DSP are much more expensive.
Here is a link to one of those sales:
If you have any questioons about those MC3810, give a holler