Complexity of codes for Ramsey positive sets

Sabok showed that the set of codes for $G_\delta$ Ramsey positive subsets of $[\omega]^\omega$ is $\mathbf{\Sigma}^1_2$-complete. We extend this result by providing sufficient conditions for the set of codes for $G_\delta$ Ramsey positive subsets of an arbitrary topological Ramsey space to be $\mathbf{\Sigma}^1_2$-complete.