Maryj,
Discuss this with your parish priest. You can look up these canons on the internet so you’ll have an idea of what is involved, but rely on that discussion. Keep in mind that the Catechism itself is not the legal text of Church law. The code of canon law is.
There is a distinction in canon law between a permission, which is usually needed for something to be lawful, and a dispensation, which is needed not only for something to be lawful but also to be valid as well.
The form of the celebration, the place of the celebration, and the condition of the other person are three different issues.
- The form of the celebration
For a non catholic ceremony, the dispensation from the canonical form mentioned canon 1127 §2 is normally required for the validity of marriage. (We’d look there rather than to canon 1112 §1, which is a little off topic here. If a non Catholic wedding is allowed, the officient would not be the delegated Catholic lay minister mentioned in that canon.). One exception would be that it is required for a lawful marriage to an “Eastern” Orthodox according to the rites of the Orthodox Church but not for validity. There are other more technical exceptions you can discuss with the priest if he believes they would seem to apply.
- The place of the celebration.
The norms for the place of celebration of a mixed marriage or the marriage of two Catholics and the permissions are found in canon 1118. These are not dispensations per se, just permissions.
- The condition of the other party to the marriage.
The permission to marry (it is not a dispensation per se) a non Catholic is found in canon 1124. Certain conditions must be met for this permission to be given.
However, if the other party is not baptized as well as being a non Catholic, then an additional dispensation from the impediment of disparity of cult mentioned in canon 1086 §1 is necessary for the validity of marriage. Certain conditions must be met for this permission to be given.