I'm afraid not. The "Buran" space shuttle started life as the BTC/BOR-5 program (a shorter version) and that was still under Myasishchev, but I believe that most later shuttle projects were from other design bureaus, with Myasishchev only designing the carrier aircraft.
Much earlier, in 1957-58, Myasishchev worked on their very first space program, a little star-shaped single hypersonic research orbiter, tentatively fitted with R-7 rockets (Model M-46 in the first M-series). Estimated altitude was not over 120-130 km. This was also studied as a rocket variant space bomber. Then in 1958-60, Myasishchev followed with the VKA-23 "Мини-Шаттл" (Mini-Shuttle) project (Model M-48), a winged reusable spacecraft to be launched by a R-7 booster and developed with Korolev and Keldysh. Like most Myasishchev programs, however, it never left the drawing board.
In the late 1990s, the company was involved in a space tourism shuttle program designated M-91 (in the second M-series) and supposed to be carried on the back of a 3M aircraft (last known number in the "EMZ" series before the Molniya era).
A more recent project was the Molniya-1000 "Herakles", a large transport which I have not seen associated with shuttle type craft, but I believe it could have served that purpose too.
Enclosed: M-91 (2 pictures), Molniya-1000, M-46 (two pictures), M-48 (3 pictures, two different projects)