`x = 21372, y = 172, rule = B3/S23`

21368bo$21368bo$21369b2o$21371bo$21371bo$21324bo46bo$21325bo45bo$

21326bo$21325bo$21324bo$21326b3o151$70b2o$71bo$8b2o$9bo5$o$o$o!

Its bounding box is 21,372 x 172. It uses the same ideas as previous 26 cell quadratic (side glider emitting switch engine pair + forward glider switch engine), but instead of generating from scratch the Glider-producing switch engine it uses a MWSS as ignition trigger (of 9 cell pattern), and pretty different side emitting switch engine, that fires MWSS at some point of it's initial stages.

EDIT Found it! 24 cell quadratic using similar trick, 24 is probably the minimum quantity reached by this trick alone.

`x = 52425, y = 52256, rule = B3/S23`

2bo$obo$b2o26283$26287bo$26287bo$26287bo25954$52419b3o$52420bo2bo$

52424bo$52421bobo8$52381b3o$52382bo2bo$52386bo$52383bobo!

EDIT2 Here is a much smaller 24 cells quadratic (judging by bounding box area):

`x = 39786, y = 143, rule = B3/S23`

39782bo$39782bo$39783b2o$39785bo$39785bo$39738bo46bo$39739bo45bo$

39740bo$39739bo$39738bo$39740b3o101$2o$o28$19bo$18b3o$20bo!

EDIT3 Here is 23 cells quadratic, I call it switch engine ping pong:

`x = 210515, y = 183739, rule = B3/S23`

1148bo$1148b2o1076$145bo$144bo$144b3o158$3bo$b2o$o$bo182353$210513bo$

210512bo$210512b3o141$210354bo$210353b3o$210355bo!