Public discourse in Kazakhstan is moving online and into the Kazakh language, yet resources for detecting toxic comments in that language remain scarce. The Kazakh corpora that exist were assembled from lists of hostile keywords within an extremism or model-safety frame, few of them are openly released, and fewer still document how they were annotated. This paper presents Kaz-ToCo, a corpus of 84,940 comments in Kazakh and in mixed Kazakh-Russian code-switched text. The comments were retrieved in May 2026 through the YouTube Data API v3 from beneath 30 Kazakhstani talk-show videos, with no keyword-based filtering at any stage of collection, and were labelled on a binary toxicity scale by an open-weight large language model deployed on local hardware. Agreement between the machine labels and the annotations of a native speaker of Kazakh, measured on a stratified sample of 100 comments, reached a Cohen kappa coefficient of 0.602, with a 95 percent confidence interval from 0.446 to 0.758. The training, validation and test splits were built at the level of the source video, which prevents comments from one video from appearing in more than one split. Two baseline classifiers are established on the corpus: term frequency and inverse document frequency features over word and character n-grams combined with logistic regression, and a fine-tuned Kazakh conversational encoder of the RoBERTa architecture. Macro-averaged F1 on the held-out test set reached 0.8086 and 0.8198 respectively. These figures fall well below the near-ceiling accuracies published on keyword-collected Kazakh corpora, and are offered as a realistic reference point. The labels, per-comment metadata, splitting protocol, random seeds and hyperparameters are released without restriction. The comment texts cannot be redistributed under the YouTube API Services Developer Policies and are available from the corresponding author upon reasonable request for non-commercial research use.