i'm afraid the previous answer is incorrect.
so you understand the concept, i will explain why it is choice A.
present participle: a verb used as an adjective to describe a noun
choice A: barking is an adjective acting as a verb
choice B: a gerund is only used as a noun
choice C: running is a verb in the sentence, not an adjective
choice D: running in the sentence is not a past participle
:)