Building physical simulations from video requires coding agents to translate observations into executable models and refine them through tool use. We introduce PhysCodeGym, a benchmark for physically verifiable 4D reconstruction with $156$ tasks covering rigid-body, liquid, deformable, and wind-driven motion. Agents autonomously inspect videos, write and run Blender programs, and revise their scenes using simulation feedback. Six metrics combine rule-based measurements with rubric-based judgments to assess visual and physical reconstruction quality. Program inspection, scene measurements, and counterfactual interventions test physical consistency under original and modified conditions. Experiments with frontier coding agents reveal a tradeoff between artifact quality and completion across reasoning-effort settings, while harness comparisons and agent traces link verification behavior with reconstruction performance. Case studies show that matching visible objects and events can coexist with physical defects. Counterfactual tests further expose latent contact and support failures in reconstructions that pass ordinary physical checks, highlighting the gap between reproducing observations and building reliable physical models. Code is available at https://github.com/ShaoShuai0605/PhysCodeGym.

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