Background: As improving code review (CR) effectiveness is a priority for many software development organizations, projects have deployed CR analytics platforms to identify potential improvement areas. The number of issues identified, which is a crucial metric to measure CR effectiveness, can be misleading if all issues are placed in the same bin. Therefore, a finer-grained classification of issues identified during CRs can provide actionable insights to improve CR effectiveness. Although a recent work by Fregnan et al. proposed automated models to classify CR-induced changes, we have noticed two potential improvement areas -- i) classifying comments that do not induce changes and ii) using deep neural networks (DNN) in conjunction with code context to improve performances. Aims: This study aims to develop an automated CR comment classifier that leverages DNN models to achieve a more reliable performance than Fregnan et al. Method: Using a manually labeled dataset of 1,828 CR comments, we trained and evaluated supervised learning-based DNN models leveraging code context, comment text, and a set of code metrics to classify CR comments into one of the five high-level categories proposed by Turzo and Bosu. Results: Based on our 10-fold cross-validation-based evaluations of multiple combinations of tokenization approaches, we found a model using CodeBERT achieving the best accuracy of 59.3%. Our approach outperforms Fregnan et al.'s approach by achieving 18.7% higher accuracy. Conclusion: Besides facilitating improved CR analytics, our proposed model can be useful for developers in prioritizing code review feedback and selecting reviewers.