XLRI has a really good reputation that it is known to uphold. Plus, it also has a decent ranking too. It would be quite difficult to maintain these two if the college had management quota.
If you are planning to seek admission here, there will be no backdoor entry. You will have to appear for the XAT and present the score for the selection process of the PGDM program. There is a 6 step process for admission to this program:
Thus, you will have to go through this 6 step procedure if you plan to seek admission to XLRI. There is no management quota.