Barrier for kikuyu

Previously kikuyu has come under the border, invaded the mulch and then got deep into the beds and the roots of my plants before I was able to get on top of it. As advised on a forum somewhere I’ve dug a 30cm trench and lined with sturdy builders polythene. However, I’m unsure of the best way to secure it. If I leave the bricks on top as shown, the kikuyu will invade between the plastic and the bricks. My intention is to bring the plastic sheet up and put a heavy plastic edging in front of it – I.e lawn > plastic edging > polythene sheet > garden and mulch. This also seems flawed as the rhizomes and stolons will work their way under the edging between the edging and the plastic. I did wonder about setting the bricks in mortar on top of the plastic but how deep would the foundations need to be to make this stable?

Long question sorry – appreciate any advice.