Federated learning (FL) is a distributed learning framework where users train a global model by exchanging local model updates with a server instead of raw datasets, preserving data privacy and reducing communication overhead. However, the latency grows with the number of users and the model size, impeding the successful FL over traditional wireless networks with orthogonal access. Cell-free massive multiple-input multiple-output (CFmMIMO) is a promising solution to serve numerous users on the same time/frequency resource with similar rates. This architecture greatly reduces uplink latency through spatial multiplexing but does not take application characteristics into account. In this paper, we co-optimize the physical layer with the FL application to mitigate the straggler effect. We introduce a novel adaptive mixed-resolution quantization scheme of the local gradient vector updates, where only the most essential entries are given high resolution. Thereafter, we propose a dynamic uplink power control scheme to manage the varying user rates and mitigate the straggler effect. The numerical results demonstrate that the proposed method achieves test accuracy comparable to classic FL while reducing communication overhead by at least 93% on the CIFAR-10, CIFAR-100, and Fashion-MNIST datasets. We compare our methods against AQUILA, Top-q, and LAQ, using the max-sum rate and Dinkelbach power control schemes. Our approach reduces the communication overhead by 75% and achieves 10% higher test accuracy than these benchmarks within a constrained total latency budget.