We study variants of Shors code that are adept at handling single-axis correlated idling errors, which are commonly observed in many quantum systems. By using the repetition code structure of the Shors code basis states, we calculate the logical channel applied to the encoded information when subjected to coherent and correlated single qubit idling errors, followed by stabilizer measurement. Changing the signs of the stabilizer generators allows us to change how the coherent errors interfere, leading to a quantum error correcting code which performs as well as a classical repetition code of equivalent distance against these errors. We demonstrate a factor of 4 improvement of the logical memory in a distance-3 logical qubit implemented on a trapped-ion quantum computer. Even-distan
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