In this work, we discuss the problem of unsourced random access (URA) over a Gaussian multiple access channel (GMAC). To address the challenges posed by emerging massive machine-type connectivity, URA reframes multiple access as a coding-theoretic problem. The sparse code-oriented schemes are highly valued because they are widely used in existing protocols, making their implementation require only minimal changes to current networks. However, drawbacks such as the heavy reliance on extrinsic feedback from powerful channel codes and the lack of transmission robustness pose obstacles to the development of sparse codes. To address these drawbacks, a novel sparse code structure based on a universally applicable power division strategy is proposed. Comprehensive numerical results validate the effectiveness of the proposed scheme. Specifically, by employing the proposed power division method, which is derived analytically and does not require extensive simulations, a performance improvement of approximately 2.8 dB is achieved compared to schemes with identical channel code setups.