Sharing source code for a HEP experiment is not that easy or possible at sometimes. A lot of stuff is done by different group and whole framework used and overall a lot of raw data collected and reconstructed involved. To analyze those even if available you willl need a lot of people with a lot of resources. So even it made available (which would be a lot of efforts itself) it wouldn't make much sense for replication purpose.
How is it possible to peer review a paper when the only people qualified to do so are the one's involved in the research. Seems like a massive issue. Don't want to cast to much shade here, but there's a fair number of people that called out high energy physics for having problematic methodology. See Constructing quarks by Andrew Pickering. Ultimately, it should be CERNS job to release the data, yes even if it is terabytes in size, because that's the whole point of science.