Using the standard lookback payoff formulas:

• Floating lookback call = $S_T - S_{\min}$
• Floating lookback put = $S_{\max} - S_T$
• Fixed lookback call = $\max(S_{\max} - K, 0)$
• Fixed lookback put = $\max(K - S_{\min}, 0)$

With the given path:

• Floating call = $76.55 - 23.58 = 52.97$
• Floating put = $89.55 - 76.55 = 13.00$
• Fixed call = $89.55 - 30.00 = 59.55$
• Fixed put = $30.00 - 23.58 = 6.42$

The highest payoff is from the fixed lookback call.