An acoustic model, trained on a significant amount of unlabeled data, consists of a self-supervised learned speech representation useful for solving downstream tasks, perhaps after a fine-tuning of the model in the respective downstream task. In this work, we build an acoustic model of Brazilian Portuguese Speech through a Transformer neural network. This model was pretrained on more than $800$ hours of Brazilian Portuguese Speech, using a combination of pretraining techniques. Using a labeled dataset collected for the detection of respiratory insufficiency in Brazilian Portuguese speakers, we fine-tune the pretrained Transformer neural network on the following tasks: respiratory insufficiency detection, gender recognition and age group classification. We compare the performance of pretrained Transformers on these tasks with that of Transformers without previous pretraining, noting a significant improvement. In particular, the performance of respiratory insufficiency detection obtains the best reported results so far, indicating this kind of acoustic model as a promising tool for speech-as-biomarker approach. Moreover, the performance of gender recognition is comparable to the state of the art models in English.