This paper examines the structural patterns in emoji sequences used in social media messages, focusing on identifying potential syntactic relationships in their arrangement. Although many emoji sequences on social platforms tend to be repetitive, some studies suggest that non-repeating emoji combinations may exhibit syntactic structure. This research explores the complexities of emoji-based communication and its possible parallels to traditional linguistic constructs, shedding light on the evolving nature of digital expression in online environments. This study concludes that the concepts of emoji grammar and emojis as digital gestures are complementary rather than mutually exclusive. To conduct this analysis, we gathered over 1.6 billion tweets spanning from 2006 to 2023, eliminating retweets and quoted tweets, and analyzed the co-occurrence of non-repeating emojis. The meaning of these emoji sequences was interpreted using BabelNet definitions, as recommended by EmojiNet. At the same time, the semantic context of the messages was extracted using keyphrases identified through Stanford CoreNLP's part-of-speech tagging. The co-occurrence data and associated keyphrases were stored in a graph database, as outlined in the Emoji Semantic Extractor framework. Our findings reveal that users exhibit syntactic awareness when using non-repeating emoji co-occurrences, with the most common syntactic patterns being verb-object, object-verb, verb-subject, and subject-verb. These results suggest that emojis can function within a grammatical framework similar to traditional language, bridging the gap between emoji grammar and digital gestures.