If the people in the organisation run like headless chickens and complain of not having enough time to do a quality job, the problem can be the lack of time. Lack of time causes quality problems in the produced code. When people hurry, they make mistakes. Released mistakes cause rework. The organisation can be said to be thrashing. The need for rework causes people to be even busier, which causes even more code that needs reworking. The organisation's productivity diminishes.
What you need is more time for quality. A quality timeout. You need to take the time and use it to deal with the quality problems. You don't need to take much, as long as you'll take it regularly and use it wisely. Taking time to perform regular code inspections is certainly going to prove its worth quickly.
The Qualiteers Code Inspection technique is efficient, already an hour is enough to produce valuable results. It is effective, since the findings directly improve the maintainability, readability and understandability of the code base. What actually happens is you'll decrease the amount of trashing and reinvest it in the quality check. Instead of wasting time producing bad software, you'll make sure that what gets produced stays produced. The productivity increase comes from minimising the rework, although at first it might seem that less code gets produced.