If your null hypothesis is that the event of being selected by your program is statistically independent from the event of being non-coding, you can use Fisher's exact test to reject the null hypothesis.
Suppose you have 10,000 (I'm making that up but presumably you have the real number) total sequences, 8,700 coding and 1,300 noncoding. Given that your program selects 728 sequences, you would expect around 13%*728 ~= 95 noncoding sequences. But your program picked 131 noncoding sequences and you want to know if 131 is far enough away from 95 to conclude that the difference is not just due to chance.
The probability of selecting 131 or more of these noncoding sequences (given that we are choosing 728 total sequences) is given by the so-called hypergeometric distribution. The two-sided test will also incorporate the probably of getting an equally unlikely low number (in this case, somewhere around 57) or less.
In R for example, you can calculate this using the 2-by-2 contingency table as follows:
fisher.test(rbind(c(597, 131), c(8103, 1169)))
p-value = 7.399e-05
So in this situation (and assuming the probability model described), there's around a 0.0074% chance of observing a ratio as "extreme" as the one you observed, which indicates it's unlikely that the two events are independent.
Note: As others have mentioned, a binomial test could be appropriate too. If your number of total sequences is very large, then the two results will converge. But if it isn't, then Fisher's exact test will be more appropriate (essentially since you're sampling without replacement).