Which document did the Pilgrims write and sign as a plan of government that said they would have "just and equal laws . . . for the general good of the colony"?

The document you are referring to is known as the Mayflower Compact. In November of 1620, the Mayflower had landed at Cape Cod in what would become the Colony of Massachusetts. There were 102 passengers on board. Only forty-one of these passengers were the religious dissenters known as Pilgrims. The rest were craftsmen, merchants, mercenaries, and indentured servants. The Pilgrims referred to these people as Strangers.
The necessity for a document defining a local government came up shortly after landing at Cape Cod. Their original destination had been Virginia, but navigational error had brought them well off course. Now they found themselves well outside the protections of the English government. A conflict between the Strangers and the Pilgrims soon arose as the former group began arguing that, since they were outside the jurisdiction of the Virginia Colony, the laws of the colonial government no longer applied. There threatened to be a rift between the two groups that could sabotage the whole venture.
To avoid this calamity, the leaders aboard the Mayflower decided it was necessary to make a mutual agreement between all the parties. They would need to create a governing body that would recognize the rights and duties of the colonists and create a means to prevent internal turmoil.
The Mayflower Compact was a tool to create a self-governing body. In England, the authority to rule came from the monarchy. Isolated across the Atlantic Ocean, the colonists aboard the Mayflower had to rely on themselves. The Mayflower Compact still affirmed them to be loyal subjects of the English king but also set up a system of governors and ministers to safeguard the civil and religious rights of the passengers. The document is relatively short, but it bound the colonists into a single civic unit created to protect the "general good of the colony." It was signed on November 11, 1620 on board the Mayflower by the adult males on board. It became the first legal document drafted by colonists in North America.
https://historyofmassachusetts.org/the-mayflower-compact/