Storing digital data in synthetic DNA faces challenges in ensuring data reliability in the presence of edit errors--deletions, insertions, and substitutions--that occur randomly during various stages of the storage process. Current limitations in DNA synthesis technology also impose the use of short DNA sequences, highlighting the particular need for short edit-correcting codes. Motivated by these factors, we introduce a systematic code designed to correct random edits while adhering to typical length constraints in DNA storage. We evaluate its performance both theoretically and through simulations, and assess its integration within a DNA storage framework, revealing promising results.