There’s two components to our justification – removal of our guilt and imputation of righteousness.  Christ’s suffering and death for our sin resolves the first and His perfect life provides us the second.  Charles Spurgeon describes our imputed righteous well as part of a sermon in Chapel Library’s Free Grace Broadcaster article:

The promises in the Word of God are not made to suffering; they are made to obedience.  Consequently, Christ’s sufferings, though they may remove the penalty of sin, do not alone make me the inheritor of the promise.  “If You will enter into life,” said Christ, “keep the commandments” (Matthew 19:17).  It is only Christi’s keeping the commandments that entitles me to enter life. “The Lord is well pleased for his righteousness’ sake; he will magnify the law, and make it honorable” (Isaiah 42:21).  I do not enter into life by virtue of His sufferings – those deliver me from death, those purge me from filthiness; but entering the enjoyments of the life eternal must be the result of obedience.  As it cannot be the result of mine, it is the result of His, which is imputed to me….See what Christ has done in His living and His dying, His acts becoming our acts and His righteousness being imputed to us, so that we are rewarded as if we are righteous, while He was punished as though He had been guilty.

Justification then comes to sinners as an act of pure grace, the foundation of it being Christ’s righteousness.  The practical way of its application is by faith. The sinner believes God and believeth that Christ is sent of God. [He] takes Christ Jesus to be his only  confidence and trust; and by that act, he becomes a justified soul. It is not by repenting that we are justified, but by believing; it is not by deep experience of the guilt of sin; it is not by bitter pangs and throes under the temptations of Satan; it is not by mortification of the body, nor by the renunciation of self; all these are good, but the act that justifieth is a look at Christ. We, having nothing, being nothing, boasting of nothing, but being utterly emptied, do look to Him Whose wounds stream with the life-giving blood. As we look to Him, we live and are justified by His life. There is life in a look at the crucified One—life in the sense of justification.