@Sébastien Perin I was working on a GLIBC issue a few weeks ago. When I ran ldd --version it returned that version 2.28 was installed on the image. It might be worth checking to see if GLIBC is installed on your image, and if so, you may simply need to adjust your version number.
Azure does support the ability to bring custom container images. This customization though is done outside of Azure. We support custom images from a couple of resources but since you mentioned Docker, I will include a few links on how to customize an image.
The docker images that App Services has published can be found here. You can use this to access the same images we use and customize them to your liking.
Once you have settled on a Docker image, I would suggest checking out Docker's resources on getting started, which can be found here.
After you have your customized image ready to go, you can follow these steps to get going with your image in Azure. This quickstart uses Azure Container Registry but Web App Containers supports multiple services.
After following these steps and guidelines, please let us know if there are any specific questions or issues you run into regarding this matter.