  We introduce a definition for \emph{Families of Optimal Binary Non-MDS
Erasure Codes} for $[n, k]$ codes over $GF(2)$, and propose an algorithm for
finding those families by using hill climbing techniques over Balanced XOR
codes. Due to the hill climbing search, those families of codes have always
better decoding probability than the codes generated in a typical Random Linear
Network Coding scenario, i.e., random linear codes. We also show a surprising
result that for small values of $k$, the decoding probability of our codes in
$GF(2)$ is very close to the decoding probability of the codes obtained by
Random Linear Network Coding but in the higher finite field $GF(4)$.
