Thomas, seems like transaction manager can't be obtained with out of the box mechanism, what you could try is to set transaction manager in environment in the same way as for JUnit tests:
- use initial context look up if you know JNDI name where transaction manager is bound to on WebLogic
- use TransactionHelper class from WebLogic to obtain it
BTW, can you find following log entry just after exception that you shared with us:
JTA TransactionManager found at fallback JNDI location
HTH