Shutter speed is fine. It's all about the lens and possibly a useless UV filter (if there).
I'd close down the aperture for this as an alternate attempt. Leave the SS the same.

Your EXIF...
Camera Model: Canon EOS REBEL T2i
Focal Length: 18.0mm
Aperture: f/5.6 <<< try f/11 or f/16
Exposure Time: 142.000 s
ISO equiv: 100
Exposure Bias: none
Metering Mode: Matrix
Exposure Mode: Manual
White Balance: Auto
Flash Fired: No (enforced)
Color Space: sRGB