General Meaning:
* Interpret
* Understand
* Explain
* Analyze
* Deem
* Consider
* See
* Take (as in "take something to mean")
Meaning: To interpret in a particular way, often negatively:
* Misinterpret
* Misunderstand
* Distort
* Twist
* Misrepresent
* Pervert
Meaning: To construct or build:
* Build
* Form
* Create
* Compose
The best synonym for "construe" will depend on the specific context and the nuance you want to convey.