The answer is a bit odd -- you can install the receptacle according to Code (ampacity-wise, it's no different than a duplex 5-15R on a 20A 120VAC circuit), according to table 210.21(B)(3) (or the summary Table 210.24 Speedy posted).
However, table 210.21(B)(2) limits you to a maximum of 12A for the entire duplex receptacle, and 210.6(A):
(A) Occupancy Limitation. In dwelling units and guest rooms or guest suites
of hotels, motels, and similar occupancies, the voltage shall not exceed 120
volts, nominal, between conductors that supply the terminals of the following:
(2) Cord-and-plug-connected loads 1440 volt-amperes, nominal, or less or less
than 1/4 hp
means that you cannot plug a single cord-and-plug connected load 6A or less into the receptacle without violating the NEC, which makes a duplex 6-15R outlet a bit less useful as you wind up with two >6A loads plugged in, only one of which can be on at a time.
Unfortunately, a 6-20T doesn't quite get you out of this mess, either, as you can only pull 16A max from it as per table 210.21(B)(2), and the definition of "single receptacle" in Art. 100:
Receptacle. A receptacle is a contact device installed at the outlet for
the connection of an attachment plug. A single receptacle is a single contact
device with no other contact device on the same yoke. A multiple receptacle is
two or more contact devices on the same yoke.
means that even though you are only putting one receptacle device on the circuit, it is still treated as multiple receptacles by the Code.
As a suggestion, I'd label this receptacle with "Do not use loads less than 6A @ 240V or 1440W" as a reminder to the next person who inhabits your house, and also check with your AHJ as to whether 210.6(A) applies to your situation; if it doesn't, there's no need for the label :)