The generator matrix

 1  0  0  1  1  1  X  1 X^2+X  1  1  1 X^2 X^2+X X^2+X X^2  1  1 X^2+X  1  1 X^2+X  1  0  1  1  X  1 X^2  1  1  1  0  1  X  1  1  1 X^2  1  0  1  0  X  1  1  1  1  X  1  1  1  1  X  1  1  1  X
 0  1  0 X^2 X^2+1  1  1  0  0 X^2 X^2+1  1  1  1 X^2+X  X  X X^2+X+1  1 X^2+X X+1  1  X  1 X^2+X+1  0  1 X^2+X  1 X+1 X^2+1  X  1 X+1 X^2 X^2+X+1  0  1  1 X^2+X+1  1 X^2+X  1  1  0  X X^2+X X+1 X^2+X X^2  0  X  X  0 X^2 X^2 X^2 X^2+X
 0  0  1 X^2+X+1 X+1 X^2 X^2+1  X  1  1 X^2+1 X^2+X  X X+1  1  1  X  1  X X^2 X+1 X^2  1 X^2+X+1  X X^2+1 X^2+X+1 X+1  1 X^2+X  0 X^2+X+1 X^2+1  0  X X^2 X^2+X+1 X^2+1 X^2 X+1 X^2+X  1 X+1  1 X^2 X^2 X^2+X X^2  1  X X^2+X  0 X^2+1  1 X^2+1 X^2+X+1  1  0

generates a code of length 58 over Z2[X]/(X^3) who´s minimum homogenous weight is 56.

Homogenous weight enumerator: w(x)=1x^0+282x^56+48x^58+132x^60+16x^62+15x^64+12x^68+6x^72

The gray image is a linear code over GF(2) with n=232, k=9 and d=112.
As d=113 is an upper bound for linear (232,9,2)-codes, this code is optimal over Z2[X]/(X^3) for dimension 9.
This code was found by Heurico 1.16 in 6.78 seconds.