We study the holographic quantum error correcting code properties of a Sierpinski triangle-shaped boundary subregion in ${\mathrm{AdS}}_4/{\mathrm{CFT}}_3$. Due to existing no-go theorems in topological quantum error correction regarding fractal noise, this gives holographic codes a specific advantage over topological codes. We then further argue that a boundary subregion in the shape of the Sierpinski gasket in ${\mathrm{AdS}}_5/{\mathrm{CFT}}_4$ does not possess these holographic quantum error correction properties.