Diabetic Retinopathy (DR) is one of the leading causes of vision impairment and blindness globally, necessitating early and accurate detection for timely clinical intervention. This paper proposes NGCF-RVFL, a novel Computer-aided-diagnosis system for multi-grade DR detection from retinal fundus images. The working of this system begins with an enhanced preprocessing pipeline that includes median filtering, Gaussian filtering, and Contrast-limited adaptive histogram equalization to reduce noise and improve contrast of the fundus images. Next, we introduce an adaptive image augmentation technique to address the issue of class imbalance. Minority class samples are increased using an augmentation that adapts the size of majority class samples. After that, we propose a Next Generation Convolutional Feature (NGCF) based on the fine-tuned ConvNeXt architecture, consisting of a hierarchical design with four feature extraction stages utilizing depthwise separable convolutions. The NGCF feature effectively encodes intricate retinal structures and disease patterns crucial for accurate DR grading. Further, the discriminative analysis with Principal Component Analysis confirms the significance and effectiveness of the extracted NGC feature in representing relevant retinal information. Furthermore, a lightweight network, Random Vector Functional Link (RVFL), is employed to evaluate the grade-wise detection performance of the proposed NGCF feature. Unlike traditional iterative learning models, the RVFL utilizes a single-pass training mechanism, significantly reducing computation time while maintaining high detection performance. Finally, we evaluate the effectiveness and detection performance of the NGCF feature on other machine learning classifiers such as Support vector machine, Multilayer perceptron, Random forest, and Decision tree. Comprehensive experiments on a benchmark dataset demonstrate that NGCF-RVFL achieves competitive scores across all DR grades with minimal training time, outperforming the state-of-the-art approaches.