This paper describes TransCore, the NewTranx submission to the WMT26 General Machine Translation Shared Task constrained track. Our system is built upon the Qwen3-8B large language model and adopts a two-stage supervised fine-tuning framework trained exclusively on publicly available data. Our approach focuses on high-quality multilingual data construction, including parallel corpus construction, knowledge-distilled corpus construction, and instruction-following data construction. For the parallel corpus, we construct a high-quality multilingual training corpus through multilingual data collection and automatic quality filtering. For knowledge distillation, we construct a KD corpus from publicly available monolingual resources using a large language model, followed by automatic quality filtering. To support the instruction-following evaluation introduced in WMT26, we further construct instruction data covering immutable entity preservation, document-level translation, and structured translation, which are incorporated into the first-stage supervised fine-tuning. Our system participates in four language directions of the WMT26 General Machine Translation Shared Task: English$\rightarrow$Indonesian, English$\rightarrow$Kazakh, English$\rightarrow$Thai, and Chinese$\rightarrow$Japanese.