We present structural properties of linear codes over the ring Z2m +vZ2m where v² = v as a generalization of specific Gao's results for the ring Z4+vZ4 where v² = v: First, we study a structure of the ring Z2m + vZ2m where v² = v and properties of linear codes over this ring, via a Gray map. Further, we consider MacWilliams relations, MDS codes, as well as Euclidean self-dual codes over this ring.