The standard BL2CK 1.31.0 kernel will allow launching TWiLight Menu++ but with the included DLDI (ak2sd.dldi) when you enter the settings menu and make changes, upon exit the changes will not be saved. Also game loading is affected adversely. Say I load my Castlevania Portrait of Ruin game, the game launches fine but if I exit and load my Metal Slug 7 game Castlevania loads instead.
The same issue occurs with the R4 SDHC 2024 (Black cartridge) from r4isdhc.hk carts (also R4DS Pro clones). The other color carts are DSTT clones for some reason.