Recursive Feature Elimination (RFE) with Logistic Regression and little correlation between the features and the target (SKLearn)
Do you think I implemented the code in the right way?


Code is correct, but he is minimal possible. 


  The features (X) have low correlation with the labels (Y).


It's could be the biggest problem, features have to have correlation with labels.


  Do you have any suggestion to enhance the accuracy? 



Make transformation of labels(X). Preparing of labels its one most important parts in Machine Learning. Please read data transformation or feature extraction.
After this try different algorithms like xgboost, adaboost, random forest etc.
Perhaps you should use regularization L1 or L2.
Try early stopping.
After this step use cross-validation.
Choose suitable metrics for yours problem.