Enforcing distinct number of trailing spaces
I wouldn't call this a good solution but it seems to work. You can create a computed column with an appended character and create a unique index on code_type and the computed column. For the appended character you can use a character which will never appear in your data or any string of at least 31 character length if you'd like to avoid making assumptions like that. It's probably easiest to go through an example.

This is the problem that you're having:

CREATE TABLE dbo.T226714 (
    code_type CHAR(4) NOT NULL,
    code VARCHAR(30) NOT NULL,
    PRIMARY KEY (code_type, code)
);

-- fails due to PK error
INSERT INTO dbo.T226714 VALUES ('cha', ' ');
INSERT INTO dbo.T226714 VALUES ('cha', '');


Instead, do something like this:

DROP TABLE dbo.T226714;

CREATE TABLE dbo.T226714 (
    code_type CHAR(4) NOT NULL,
    code VARCHAR(30) NOT NULL,
    code_with_end_char AS CAST(code + 'ZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZ' AS VARCHAR(61))
);

CREATE UNIQUE INDEX UI ON dbo.T226714 (code_type, code_with_end_char);

-- works
INSERT INTO dbo.T226714 VALUES ('cha', ' ');
INSERT INTO dbo.T226714 VALUES ('cha', '');

-- can't insert this as a third row due to the unique index:
INSERT INTO dbo.T226714 VALUES ('cha', ' ');