Continuous verb forms are to be + -ing form of verb.
A transitive verb is a verb that requires a direct object.
They exist together without issue.
I kicked the ball.
I am kicking the ball.
However, just because you see an -ing word does not mean it's continuous tense, a form of to be must precede it.
This implicates finding a common language.
Implicates is not a continuous tense here. The continuous form of this sentence would be This is implicating finding a common language.
So you are not really asking about present continuous tense.
What you are doing here is using a verb as an noun, and that noun is falling in the same place as an object. When you do this, you may need to use the plain verb form, the full infinitive form "to X", or the -ing form of the verb.
The rules on which to choose are complex (for example, after want you would normally use the full infinitive - e.g. I want to go to the park.) Look at this for further help.
In this situation you should use the -ing form of the verb as you've done in your second sentence.