Here is a list of all quantum codes useful for distilling magic states and characterized by their magic-state distillation scaling exponent.
Name Magic-state scaling exponent
H code A total of $$r$$ rounds of magic-state distillation yields a magic-state scaling exponent $$\gamma\to 1$$ as $$k,r\rightarrow \infty$$. This matches a conjectured bound for $$\gamma$$ [1].
Triorthogonal code Depends on the matrix. Reference [1] gave a family of $$\frac{k}{3k+8}$$ codes with magic-state distillation scaling exponent $$\gamma = \log_2 \frac{3k+8}{k}$$.
$$[[15,1,3]]$$ quantum Reed-Muller code Magic-state distillation scaling exponent $$\gamma= \log_d (n/k)\approx 2.46$$ [2].

## References

[1]
S. Bravyi and J. Haah, “Magic-state distillation with low overhead”, Physical Review A 86, (2012). DOI; 1209.2426
[2]
J. Haah et al., “Magic state distillation with low space overhead and optimal asymptotic input count”, Quantum 1, 31 (2017). DOI; 1703.07847