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Image Coding for Machines (ICM) aims to compress images for AI tasks analysis rather than meeting human perception. Learning a kind of feature that is both general (for AI tasks) and compact (for compression) is pivotal for its success. In this paper, we attempt to develop an ICM framework by learning universal features while also considering compression. We name such features as omnipotent features and the corresponding framework as Omni-ICM. Considering self-supervised learning (SSL) improves feature generalization, we integrate it with the compression task into the Omni-ICM framework to learn omnipotent features. However, it is non-trivial to coordinate semantics modeling in SSL and redundancy removing in compression, so we design a novel information filtering (IF) module between them by co-optimization of instance distinguishment and entropy minimization to adaptively drop information that is weakly related to AI tasks (e.g., some texture redundancy). Different from previous task-specific solutions, Omni-ICM could directly support AI tasks analysis based on the learned omnipotent features without joint training or extra transformation. Albeit simple and intuitive, Omni-ICM significantly outperforms existing traditional and learning-based codecs on multiple fundamental vision tasks.