can blizzard use running shot in a combo with barrier?

No,

From the PAC:

"RUNNING SHOT This character can move and then make a ranged combat attack in the same action. (Optional) When you give this character a move action, he or she may move up to half his or her speed value and then make a ranged combat attack as if he or she had been given a ranged combat action. This ranged combat attack does not cost an extra action. This character may use any of his or her powers that require a ranged combat action except Ranged Combat Expert."

"BARRIER This character can create up to 4 squares of blocking terrain. (Optional) Give this character a move action, but do not move him or her. This character creates 4 squares of blocking terrain anywhere within the character’s range; if the character’s range is 0, the markers must be placed adjacent to the character. Place 4 blocking terrain markers on the map using the following guidelines: All 4 squares of blocking terrain markers must be in squares adjacent to each other, and they cannot be placed in the same space as a character, object, or terrain feature. A character cannot move or fire through the diagonal corner where two Barrier markers are touching. This Barrier uses all the standard rules for blocking terrain. This terrain is not elevated and can be flown over. This Barrier remains in place until the beginning of your next turn."

They both require a move action. If you wanted to use Running Shot and Pulse Wave then yes you could because Running Shot allows you to move then use a Ranged Combat attack which Pulse Wave is.

I hope this helps.