Improving biomedical technology leads to the collection of increasingly large amounts of -omics data. To harness this information, for instance to identify biomarkers for a given disease, efficient statistical methods are necessary. Although penalized regression methods are among the most common tools for these applications, most of the methods use the square error loss which is susceptible to outlying observations. Recently proposed penalized robust regression methods, on the other hand, either have low efficiency or require a robust and accurate estimate of the error scale to achieve the promised robustness and high efficiency. We propose a penalized regression estimator combining the robust S-loss with an adaptive elastic net penalty. We show that this estimator is variable selection consistent under weak conditions. This in turn improves the estimate of the error scale compared to non-adaptive elastic net. We demonstrate in numerical experiments that the improved error scale estimate in combination with the M-loss and the adaptive elastic net penalty yields robust and simultaneously efficient penalized estimators of regression.