I'd be tempted to go with masonry screws if it's going into brick. It's not very clear exactly what's happening since you have those T-pieces that look like they're attaching to the ceiling. If they're not going to be screwed up into a joist then I'd be pretty concerned about just wall-mounting that as it looks heavy (especially when it's covered in clothes) and the mounting plates that will fit it to the wall are small, which means lots of leverage pulling it out.
I'd be tempted to go with masonry screws if it's going into brick. It's not very clear exactly what's happening since you have those T-pieces that look like they're attaching to the ceiling. If they're not going to be screwed up into a joist then I'd be pretty concerned about just wall-mounting that as it looks heavy (especially when it's covered in clothes) and the mounting plates that will fit it to the wall are small, which means lots of leverage pulling it out.