Ferulic acid has numerous beneficial effects on human health, which are frequently attributed to its antioxidant behavior. In this report, many of them are reviewed, and 185 new ferulic acid derivatives are computationally designed using the CADMA-Chem protocol. Consequently, their chemical space was sampled and evaluated. To that purpose, selection and elimination scores were used, which are built from a set of descriptors accounting for ADME properties, toxicity, and synthetic accessibility. After the first screening, 12 derivatives were selected and further investigated. Their potential role as antioxidants was predicted from reactivity indexes directly related to the formal hydrogen atom transfer and the single electron transfer mechanisms. The best performing molecules were identified by comparisons with the parent molecule and two references: Trolox and α-tocopherol. Their potential as polygenic neuroprotectors was investigated through the interactions with enzymes directly related to the etiologies of Parkinson’s and Alzheimer’s diseases. These enzymes are acetylcholinesterase, catechol-O-methyltransferase, and monoamine oxidase B. Based on the obtained results, the most promising candidates (FA-26, FA-118, and FA-138) are proposed as multifunctional antioxidants with potential neuroprotective effects. The findings derived from this investigation are encouraging and might promote further investigations on these molecules.