POWER OF ATTORNEY

      Know all by these present, that the undersigned hereby constitutes and
appoints each of Yalonda Howze and Wendy Silverman of Codiak BioSciences, Inc.
and each of Megan Gates, Nadia Do Canto, Amanda Mei, Samantha Silver, Charles
Koech, Anne Leland and Brenda Meyette of Mintz, Levin, Cohn, Ferris, Glovsky and
Popeo, P.C., signing singly, with full power of substitution, the undersigned's
true and lawful attorney-in-fact to:

      (1)   execute for and on behalf of the undersigned, forms and
            authentication documents for EDGAR Filing Access;

      (2)   do and perform any and all acts for and on behalf of the undersigned
            which may be necessary or desirable to complete and execute any such
            forms and authentication documents;

      (3)   execute for and on behalf of the undersigned, in the undersigned's
            capacity as an officer, director and/or 10% shareholder of the
            Company, Forms 3, 4 and 5 in accordance with Section 16(a) of the
            Securities Exchange Act of 1934 and the rules thereunder;

      (4)   do and perform any and all acts for and on behalf of the undersigned
            which may be necessary or desirable to complete and execute any such
            Form 3, 4 or 5 and timely file such form with the United States
            Securities and Exchange Commission and any stock exchange or similar
            authority; and

      (5)   take any other action of any type whatsoever in connection with the
            foregoing which, in the opinion of such attorney-in-fact, may be of
            benefit to, in the best interests of, or legally required by the
            undersigned, it being understood that the documents executed by such
            attorney-in-fact on behalf of the undersigned pursuant to this Power
            of Attorney shall be in such form and shall contain such terms and
            conditions as such attorney-in-fact may approve in such attorney-in-
            fact's discretion.

      The undersigned hereby grants to each such attorney-in-fact full power and
authority to do and perform any and every act and thing whatsoever requisite,
necessary, or proper to be done in the exercise of any of the rights and powers
herein granted, as fully to all intents and purposes as the undersigned might or
could do if personally present, with full power of substitution or revocation,
hereby ratifying and confirming all that such attorney-in-fact, or such
attorney-in-fact's substitute or substitutes, shall lawfully do or cause to be
done by virtue of this power of attorney and the rights and powers herein
granted. The undersigned acknowledges that the foregoing attorneys-in-fact, in
serving in such capacity at the request of the undersigned, are not assuming,
nor is the Company assuming, any of the undersigned's responsibilities to comply
with Section 16 of the Securities Exchange Act of 1934, as amended.

      This Power of Attorney shall remain in full force and effect until the
undersigned is no longer required to file Forms 3, 4 and 5 with respect to the
undersigned's holdings of and transactions in securities issued by the Company,
unless earlier revoked by the undersigned in a signed writing delivered to the
foregoing attorneys-in-fact.

      IN WITNESS WHEREOF, the undersigned has caused this Power of Attorney to
be executed this 17th day of August, 2021.


                            /s/ Arundathy N. Pandite
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                                     Signature

                                    Arundathy N. Pandite
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                                     Print Name