This has previously been translated as "20th dimension" in the powerscaling community. However, that was a machine translation. With no official transcription for these drama CDs, translations have to rely on prior knowledge, context, and intuition.
I'm beating around the bush here, but essentially, there are two plausible interpretations for "nijuu jigen" here. Jigen is 次元 dimension either way, so I'll just focus in on nijuu.
The first interpretation is 二十, meaning twenty, so "二十次元" would be "20th dimension." There's nothing inherently wrong with this - it's how you'd say it, and Gurren Lagann likes doing funny dimension things.
The second interpretation is 二重, meaning double-layered, twofold, and so on, hence "twofold dimension." An example of 二重 that some might be aware of is Hakurei Reimu's Spell Card 二重結界, which the Touhou community translates as "Duplex Barrier."
I'm not at well-versed in TTGL as a lot of people reading this likely are, but from what I understand, official text supports up to an 11th dimension. But the point is, it's my opinion, that given the following factors...
1. Gurren Lagann's highest mentioned dimension is 11, and 11 to 20 is a huge jump for no particular reason besides "this is the evil side's final attack"
2. The sentence has a convenient "two" we can connect the concept of twofold with since two powers are beind discussed as the subject of whatever "twisting" is happening here
3. No character reacts to this in any way that supports the meaning of 20th dimension, nor is it addressed again later
4. From the Gurren Lagann Wiki, when describing Infinity Big Bang Storm: "The mech grabs two nearby Super Spiral galaxies in the Super Spiral Space, crushes them together, and compresses their matter and energy into a ball. It then unleashes the resulting pressure, combined with the Anti-Spiral's own energy, as an enormous blast of raw energy."
"Grabbing two galaxies and crushing them together" sounds an awful lot like "taking two powers and twisting them together," supporting the theory that Lordgenome is just explaining how he's using these powers as fuel for Infinity Big Bang Storm
...that twofold is more likely to be the correct interpretation for nijuu here. Furthermore, from discussions I'm seeing online, it seems that these higher dimensions are less of "dimensions" and actually more of universes? There's a LOT of text talking about this stuff and I don't claim to really understand it, but if I'm correct in taking that at face value, then there's nothing making a theoretical 20th dimension more special than the 11th dimension, making it an even stranger choice to bring up out of nowhere like this.
I'd be happy to look at and give my thoughts on any official JP text related to this topic if someone could provide it.