The assessment of computed tomography (CT) image quality has traditionally relied on manual evaluation by radiologists, a method that is both subjective and time-consuming. Deep learning-based methods usually only give quantitative scores and are not explainable. Additionally, the application of general-purpose, closed-source vision-language models (VLMs) is constrained by patient privacy regulations and the highly specialized requirements of clinical data. To overcome these limitations, we propose a parameter-efficient supervised fine-tuning (SFT) framework for the medical VLM, MedGemma-4B-IT, designed to automate CT image quality scoring and generate professional textual explanations within the clinical environment. We employed quantized low-rank adaptation (QLoRA) for parameter-efficient fine-tuning, aiming to align the model’s visual perception with expert quantitative judgment. Experimental results demonstrate that our finetuned model achieves a substantial improvement in correlation with expert scores (SRCC = 0.7950, PLCC = 0.7907), outperforming zero-shot baselines such as Gemini 2.5 Pro and Gemini 2.5 Flash. Furthermore, the model generates explainable text that emulates the reasoning and explanation style of radiologists, thereby advancing the application of eXplainable AI (XAI) in medical image analysis. The project is publicly available at https://github.com/atJesse/VLM-CT-IQA.