  We present a Monte Carlo study of the correlation length $\xi$ of randomly
diluted antiferromagnetic Heisenberg ladders, composed of two spin--1/2 chains.
For weak and intermediate inter--chain couplings, $J_{\bot}/J \leq 1$, we find
an enhancement of correlations that is strongest for a fraction $z^* \approx
J_{\bot}/(8J)$ of dilutants. We are able to access the experimentally relevant
low--temperature regime, $T/J \approx 1/500$, and find that the recently
inferred N\'eel temperature of $Sr(Cu_{1-z}Zn_z)_2O_3$ corresponds to a curve
of constant correlation length $\xi \approx 18$ of the single diluted ladder
with $J_{\bot}/J \alt 1/2$. The primary reason for the N\'eel ordering is
argued to be a strong enhancement of two--dimensional correlations due to a
Cu--Sr--Cu exchange coupling of $\approx 10 meV$ in the stacking direction of
the ladders.
