Can i run 1080p MP4 movie in ipod touch 6th generation?

Yes

The 6G supports video playback of:

• H.264 video up to 1080p, 30 frames per second, Main Profile level 4.1 with AAC-LC audio up to 160 Kbps, 48kHz, stereo audio in .m4v, .mp4, and .mov file formats
• MPEG-4 video up to 2.5 Mbps, 640 by 480 pixels, 30 frames per second, Simple Profile with AAC-LC audio up to 160 Kbps per channel, 48kHz, stereo audio in .m4v, .mp4, and .mov file formats
• Motion JPEG (M-JPEG) up to 35 Mbps, 1280 by 720 pixels, 30 frames per second, audio in ulaw, PCM stereo audio in .avi file format

from:

http://www.apple.com/shop/buy-ipod/ipod-touch