The 64 per cent entitled to free school meals reflects its remote location away from industrial centres. The reality for most school-leavers is emigration or poverty on a small family farm.
Charlie Gallen, the headteacher, knows parents and pupils well because, like nine of his teachers, he is local. He also understands the sense of rejection the 11-plus can cause because he failed the tests as a boy.
Yet there is no despondency at St Eugene's, no sense that it's battling against impossible odds, unlike some city schools with high levels of poverty. Considering that the most able pupils are creamed off by grammar schools in Strabane and Omagh, it performs well enough for the head and several teachers to send their own children there.
About one in six of the pupils got a pass in the 11-plus and one in ten got grades A or B, but the number of top pupils is falling - not as a result of any changes at St Eugene's but because open enrolment has allowed grammar schools to increase their intakes.
In the latest performance figures, the proportion of pupils getting good GCSE grades was higher than the average for Northern Ireland secondary schools.
Mr Gallen believes much of the success comes down to the role of parents: "They are very supportive of the school and very keen on their children getting a good education.
"At the meetings for parents of year eight pupils, for example, we have almost 100 per cent attendance and I give a lot of emphasis to home-school links. We are beginning a paired reading scheme to raise standards where there are difficulties."
One of the head's aims is to build up the esteem of pupils, especially boys, who account for most of the under-performance. Rather than aiming at examination results that will lead to better ratings in the annual tables, he concentrates on low achievers.
In an intake group of 60, for example, he would create a top stream of about 25 and a second of around 23, leaving only a dozen in the lowest stream. This helps to explain why only 2 per cent of pupils leave without any GCSE passes, compared with 7 per cent in secondary schools overall.
However, he believes the curriculum does not cater for the lowest ability pupil. "Selection at the age of 11 is too early. If there must be selection, it should be at the end of key stage 3 - this works quite well in Craigavon. There is too much pressure on children to succeed at an early age. What worries me are those children who are being stigmatised, perhaps for years to come, because they did not pass the11-plus.
"The role of secondary schools has not been defined. They seem to be the place where pupils who fail the selection system go, but we teach the same curriculum as grammar schools and are expected to compete with them in examination results," he said.
Mr Gallen had no definitive answer to the class bias of selection.
"People who are unemployed probably feel demoralised and find it difficult to motivate their children. In many cases both parents and children feel they are losers."