Codrington, who was lightly recruited, walked-on at North Carolina Central University in 2019, as he had several family members who had attended the school.[3] In his first year with the football team, he was mainly used as a return specialist and averaged 18.8 yards per kickoff return and 7.8 yards per punt return.[3] He was the Mid-Eastern Athletic Conference (MEAC) Specialist of the Week after returning a kickoff 75 yards for the game-winning touchdown against Delaware State and ended the season ranked third in the conference in punt return average, being named third-team All-MEAC.[3][4] He also recorded eight tackles as a defensive back.[5]
Following the 2020 season being canceled due to the COVID-19 pandemic, Codrington started the 2021 season with a game-sealing 77 yard punt return touchdown in the opener against Alcorn State.[3] He was the third-leading punt returner at the NCAA Division I FCS level in the 2021 season, with an average of 15.0 yards that also placed first in the MEAC.[5] Codrington also was second in the MEAC with an average of 22.5 yards per kick return and made 43 tackles and four pass breakups on defense.[5] He was named to Phil Steele's All-MEAC team at four different positions, being a first-team All-MEAC punt returner, third-team All-MEAC kick returner, third-team All-MEAC all-purpose player, and fourth-team All-MEAC defensive back.[5] Codrington also earned selection to the BOXTOROW HBCU All-America team at punt returner and was a one-time MEAC Specialist of the Week during the 2021 season.[5][6]
Codrington was named third-team All-MEAC at return specialist in 2022, after recording averages of 19.3 yards per kick return and 6.8 yards per punt return.[4] In his senior year, 2023, he averaged 19.6 yards per punt return and 17.9 yards per kick return, scoring two punt return touchdowns.[5] He finished his collegiate career having started 41 games, totaling 93 tackles and 10 pass breakups on defense and 2,148 return yards and four return touchdowns on 130 total returns.[5][4]
On May 6, 2024, Codrington was signed by the New York Jets as an undrafted free agent.[8] He impressed as a returner in preseason, recording a 63 yard kick return and a 31 yard punt return.[9]