Automated multiple-choice question (MCQ) generation is valuable for scalable assessment and enhanced learning experiences. How-ever, existing MCQ generation methods face challenges in ensuring plausible distractors and maintaining answer consistency. This paper intro-duces a method for MCQ generation that integrates reasoning-based explanations for both correct answers and distractors, leveraging open-source language models finetuned on publicly available datasets. Our approach addresses these issues with 3 major improvements. First, over 300k questions from public datasets were augmented with synthetically generated reasoning explanations. Second, we fine-tune a Large Language Model (LLM) with reasoning-based explanations to condition the generation while accounting for correct reasoning and possible misconceptions. Third, we introduce a multi-step filtering pipeline to ensure the validity of the question and the diversity of the generated distractors. This work argues for the effectiveness of reasoning-enhanced finetuning in improving MCQ generation quality while maintaining accessibility and cost efficiency. We release all resources, including synthetically augmented questions, training code, and the best model as open-source. [This paper was published in: "AIED 2025, LNAI 15882," edited by A. I. Cristea et al., Springer Nature Switzerland, 2025, pp. 308-15.]