In this article, we showcase PSL(3,4) as the automorphism group for a specific class of three linear binary codes C1, C2 and C3 with dimension 9. The demonstration involves leveraging the action of the group PSL(3,4), represented by invertible matrices of size 9 by 9 up to isomorphism, on the vector space F29. Additionally, we establish that these codes exhibit a 3−weight self-orthogonal property. All computations presented in this paper were conducted using guava package of GAP (Groups, Algorithms, Programming) a system designed for computational discrete algebra.