I did not make an implication, I made a statement, and I made the statement based on the testimony of the president of the corporation.
The meaning here is this one
"something that you suggest is true, although you do not say it directly"
The person speaking in that quote has been accused of making an implication, that is, implying something indirectly. His answer is that he wasn't making an implication, but a direct statement.
In the context of conversations, an implication refers to some "assertion" that's not explicitly stated, but which a speaker / writer would expect the audience / reader to understand anyway.
...from which you'll see that all the common verbs identifying the relationship between subject and object involve him receiving the implication - none of them are about him producing an implication.
TL;DR: Idiomatically, native speakers almost never make an implication - we normally just imply [whatever implication is meant].