Elastic net with increased penalty for lower quality features

Question

I’m building multinomial classification models using features characterized with high false-positive rate. Meaning, as the signal rate of the feature is lower (say gene expression abundance) the more likely it will go undetected.

I want to incorporate this information in the elastic net regression model so the lower quality features will be less likely to be selected and therefore the model will perform better on the test set as it relies on more higher quality features.

Is there a way to incorporate such information in the Glmnet R package? Or anything similar to this package?

Thanks