#Java 10, <s>120</s> <s>113</s> <s>112</s> <s>109</s> 107 bytes

<!-- language-all: lang-java -->

    n->{var r="|";for(char c,i=0;n++>0;r=n%3<1?c+r:n%3>1?r+c:r,n/=3)c=(char)(i++<1?49:i<3?51:i<4?57:i+61);return r;}

-3 bytes by using part of the trick of [*@Arnauld*'s JavaScript (ES6) answer](https://codegolf.stackexchange.com/a/160550/52210),  
changing `i=0` and `i++<1?49:i<3?51:i<4?57:i+61` to `i=4` and `++i>9?i+55:i>8?57:++i+43`.  
-2 bytes thanks to *@Arnauld* directly,  
changing `i=4` and `++i>9?i+55:i>8?57:++i+43` to `i=7` and `i++>9?i+54:i*6%13%9+49`.

Order of output: Highest-to-lowest, `|`-delimiter, lowest-to-highest.

**Explanation:**

[Try it online.](https://tio.run/##hZDBTsMwDIbvPIU1qVJCtrKqg6kNaZ@AXTgiDiHrIKNzJzethMaevZit16mWI8X5HPn/vbe9Xey334OrbdvCi/V4ugPwGCraWVfB5r8EeA3k8ROcYAIoNT@e@XC2wQbvYAMIBgZcFKfeEpCZ/c70riHhvrh0c2/WGpUqlpoMRulzUjpFOd@KpCTlcprjg0mlM5cPUnjuzUqvHle5v3@KkjTK1CqTmqrQEQLp86CvAo7dR80CRh1947dwYBviKvnt3crRwk8bqkPcdCE@Mgk1CoydWMqLm5s8meDrKZ5OTcg45LjS8/AH)

    n->{              // Method with integer parameter and String return-type
      var r="|";      //  Result-String, starting at the delimiter "|"
      for(char c=64,  //  Character
               i=7;   //  Index, starting at 7
          ;n++>0      //  Loop as long as `n` is larger than 0
                      //  Increasing it by 1 with `n++` at the start of every iteration
          ;           //    After every iteration:
           r=         //     Change the result to:
             n%3<1?   //      If `n` modulo-3 is 0:
              c+r     //       Prepend the character to the result
             :n%3>1?  //      Else-if `n` modulo-3 is 2:
              r+c     //       Append the character to the result
             :        //      Else:
              r,      //       Leave `r` unchanged
           n/=3)      //     Integer-divide `n` by 3
         c=(char)(    //   Set the character `c` to:
             i++>9?   //    If the index `i` is 10 or larger:
                      //    (and increase `i` by 1 with `i++` after checking)
              i+54    //     Set `c` to the `i-11`'th (0-indexed) letter of the UC alphabet
             :        //    Else (it's lower than 9):
              i*6%13%9+49);
                      //     Set `c` to either '1', '3' or '9' based on the index `i`
       return r;}     //  Return the result-String