I will break this down into separate points and sections.
You said that you did not mean to come out as racist, the phrase of "eat my dog" is a commonly used "joke" at the expense of those of Asian descent. This along with the knowledge of their ethnicity, you should have used the common sense to have not said this joke, I have also observed that you've never used this joke towards anyone else either.
This is without any screenshots and just going off what has been seen and said.
However with the following two screenshots, you not only make the joke multiple times towards Beignetboo, you actually single them out by @ing them in the chat to get their attention. As seen in the following screenshots:
https://cdn.discordapp.com/attachments/738832747270897664/751942565644861540/Screen_Shot_2020-08-28_at_2.17.34_PM.png
https://cdn.discordapp.com/attachments/738832747270897664/751942563598041118/Screen_Shot_2020-08-28_at_2.17.57_PM.png
In the first screenshot you can see that Beignetboo has said "thanks for being racist" of which you respond with "<3" although you could take the "thanks for being racist" as a joke, it in my opinion is more of a sarcastic response towards the racist remarks that have been made due to it being a common remark made on the internet. You response however shows that you showed no remorse or apologetic nature towards being accused of being racist.
What also makes me think you are not remorseful for this comment is your reaction to the ban and the following conversation as seen in the two screenshots below:
https://cdn.discordapp.com/attachments/738832747270897664/751943889027334167/Screen_Shot_2020-09-04_at_11.51.39_PM.png
https://cdn.discordapp.com/attachments/738832747270897664/751943889190912070/Screen_Shot_2020-09-04_at_11.51.55_PM.png
In this conversation it is seen that you claim that it was not a racist remark in nautre, and claimed that you had said it to beignetboo out of boredom. However, in the second screenshot, you can see that you then claim that beignetboo is being racist for taking offense towards the remarks, alongside you saying that you're of Asian descent in an attempt to brush off the racist nature of the remarks.
Finally within this conversation beignetboo also explains that you had singled them out with these remarks AFTER they revealed their ethnicity towards you. This final point, along with the rest of the evidence I have supplied, show that you knew what you were saying and the nature of it. Along with the fact that you are unapologetic about it in any of the conversations show that you don't have any remorse for coming across as racist too.
We have a zero tolerance nature on racism, this isn't only aimed at the users but for everyone on the server. Staff included as seen with 2 staff members being permanently banned for what they had done. Due to this, and the fact that beignetboo didn't want to permanently ban you. I'm going to revise the punishment, to a 2month ban with a final warning. This is in reflection of your actions and reaction after the initial punishment.
You shall be unbanned in 42days and you will have a final warning on your account where if you do anything like this again, you will be permanently banned.