In this paper, we explore the potential of developing an interweave cognitive radio (CR) system based on a hierarchical wide-band two-dimensional spread multi-carrier directedsequenced code division multiple access (MC-DS-CDMA). First, a small CR cell is embedded in a large primary cell such that the spatial separation gives a chance to share the spreading code resources with the primary system. Second, the white, gray and black spreading codes are defined to facilitate the management of the spreading code resources. Also, a new multiple access interference (MAI) coefficient is derived to quantize the amount of intra- and inter-system interference. Third, based on the MAI coefficient, a dynamic spectrum access (DSA) algorithm, including the code assignment/reassignment, transmission power control and call admission control mechanisms, is proposed to efficiently utilize the white and gray spreading codes without damaging the primary system. The simulation results show that compared with the the case of using only the white spreading codes, some extra 53% increase in call admissions and 13% decrease in call droppings can be attained by using the gray spreading codes properly.