Multiple Input Double Output (MIDO) asymmetric space-time codes for 4 transmit antennas and 2 receive antennas can be employed in the downlink from base stations to portable devices. Previous MIDO code constructions with low Maximum Likelihood (ML) decoding complexity, full diversity and the non-vanishing determinant (NVD) property are mostly based on cyclic division algebras. In this paper, a new family of MIDO codes with the NVD property based on crossed-product algebras over Q is introduced. Fast decodability follows naturally from the structure of the codewords which consist of four generalized Alamouti blocks. The associated ML complexity order is the lowest known for full-rate MIDO codes (O(M^{10}) instead of O(M^{16}) with respect to the real constellation size M). Numerical simulations show that these codes have a performance from comparable up to 1dB gain compared to the best known MIDO code with the same complexity.