What is the ruling on reciting a specific part of the Quran every Thursday evening and completing it before Friday prayer, with the intention of collectively ختم (completing) the Quran weekly, and does this time have any specific فضيلة (virtue)?

Each woman does not receive the reward of a complete recitation [of the Quran] by reading one juz' (part); rather, she receives the reward only for what she has read. And singling out Friday and its eve for reading a juz' from the Quran, if done with the intention of worship, it is feared that it may be an innovation (bid'ah).