Machine learning has emerged as a prominent approach to addressing various optimization problems in distributed databases, such as distribution-key recommendation, performance prediction, and parameter auto-configuration. However, the complex architecture and query execution processes of distributed databases pose significant challenges for feature selection and encoding in machine learning. Recently, several methods have been proposed that utilize physical plans or SQL queries as features. However, these methods often rely on using physical plans or SQL queries independently, neglecting the inherent characteristics of distributed databases, which limits their ability to fully represent the query features of such systems. To overcome these limitations, we introduce DISEncoder, a query feature representation model specifically designed to address various optimization challenges in distributed databases. In this approach, we utilize three types of information-execution plans, distributed database architecture, and execution process logs-to construct representations of distributed queries. This information is integrated into two graph structures, and we develop a dual-branch graph encoding model to encode and fuse these structures, resulting in a feature representation vector for queries. We incorporated DISEncoder into two machine learning models for database optimization tasks, and experimental results demonstrate that DISEncoder significantly improves the performance of these models.