Here is my answer to the question. Arrived at this solution after looking at Euler's solution(https://sites.google.com/site/tpiezas/0020). But it is not running due to timeout problem :(

import math

from itertools import combinations

def perfect_square(n):

res = int(math.sqrt(n))

return res*res == n

def check_perfect(list):

p, q, r, s = list    

if perfect_square( (p*p-q*q)*(r*r-s*s) ):    

    a = p*r + q*s    
    b = p*s - q*r
    c = p*r - q*s
    d = p*s - q*r
    x = int((a*a + b*b)/2)        
    y = int((a*a - b*b)/2)
    z = int((c*c - d*d)/2)
    if(x>y and y>z):
        print(p,q,r,s,x,y,z)

list = []

for i in range(1,int(math.pow(10,12)+1)):

if(perfect_square(i)):

    list.append(i)

for i in combinations(list, 4):

check_perfect(i)