This research proposes a novel approach to the Word Sense Disambiguation (WSD) task in the Ukrainian language based on supervised fine-tuning of a pre-trained Large Language Model (LLM) on the dataset generated in an unsupervised way to obtain better contextual embeddings for words with multiple senses. The paper presents a method for generating a new dataset for WSD evaluation in the Ukrainian language based on the SUM dictionary. We developed a comprehensive framework that facilitates the generation of WSD evaluation datasets, enables the use of different prediction strategies, LLMs, and pooling strategies, and generates multiple performance reports. Our approach shows 77,9% accuracy for lexical meaning prediction for homonyms.