Register in an LMS the highest score of 2 possible attempts

Sounds like you may need to utilize some custom variables to hold your scores, instead of the built-in quiz functionality.

Then you could apply a JavaScript trigger to check/compare the two and send the results to your LMS.

FYI - there are slightly different JS calls depending on whether you publish to SCORM 1.2 vs SCORM 2004.

Example SCORM 1.2

//get LMS API
 var lmsAPI = parent;

 //set score; the first number is the score
 //lmsApI.SetScore(yourscore, Max score, Min score);
 lmsAPI.SetScore(90, 100, 0);

 //set status; possible values: "completed", "incomplete", "failed", "passed"
 lmsApI.SetStatus("completed");

Example SCORM 2004

// get LMS API
var lmsAPI = parent;

// set score; the first number is the score
// lmsAPI.SetPointBasedScore(intScore, maxScore, intMinScore);
lmsAPI.SetPointBasedScore(100, 100, 0);

// set passed/completed
lmsAPI.SCORM2004_SetPassed();
lmsAPI.SCORM2004_SetCompleted();