If this is the entire budget for the house, then forget it.
I found a post that fits your requirements quite well and read the numbers to you:
https://www.hausbau-forum.de/threads/250000eur-baukosten-brutto-fuer-efh-im-suedlichen-bw.28732/
Can confirm that. Please do not try to build a house with the budget. That only leads to tears. With double the budget for the very small house size (without a basement) and an extremely high amount of personal contribution, there is a chance of realization.