A genetic algorithm modified for a specific problem
Start with a population, where every candidate is "good", where "good" means they contain at least one occurrence of substrings "01" and "011".

For the mutation operator, flip a coin. If the result is heads, choose a random substring of length 2 and change it to "01". If the result is tails, choose a random substring of length 3 and change it to "011".

For the crossover operator, let $A$ and $B$ be two parents. Find say the first occurrence of substring "01" or "011" from $A$, that occurs starting from index $i$. Check if in $B$ there is an occurrence of "01" or "011" before $i$. If so, choose $i$ as your crossover point. If not, find the next occurrence from $A$, and repeat. This process will terminate at some point, because you start out with individuals containing "good" substrings, and your operators maintain an invariant that all individuals are "good".

Please note that this only really answers your question of "how do I modify my GA", and does not address whether this works performance-wise. However, this should give you ideas as to what kind of operators you can experiment with.