The generator matrix

1 0 1 0 1 1 X 1 1 1 X 0 1 X 0 1 1 0 1 1 1 X 1 1 1 0 X X 1 1 1 1 1 1 X X X 1 X 0 1 1 1 X 1 X X 1 X 1 1 X 1 1 1 1
X 1 1 1 X+1 0 X 0 0 X+1 1 X 1 1 0 0 X 1 0 X+1 X+1 1 1 0 0 X X X 1 X+1 0 0 0 0 1 X 1 1 1 1 0 X X+1 1 X 0 1 0 1 X+1 0 1 X X X+1 1
X 0 0 X+1 X+1 1 1 1 X X+1 1 X 0 0 1 X+1 X X+1 1 X X+1 X 0 0 1 1 1 X X+1 1 X X+1 1 X X X 1 0 X 0 0 0 0 0 1 0 X+1 1 0 0 0 1 0 X+1 1 X
0 0 X 1 X+1 1 1 0 1 0 X 1 X+1 X+1 X 0 X 0 X+1 0 X+1 X 1 0 0 X+1 X 1 X X+1 X 1 X 1 X+1 1 X+1 X X+1 X+1 0 X+1 X 0 X 1 0 1 X 0 X+1 0 1 1 X 1
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 X X X X X X X 0 X X X X X X 0 0 X 0 X X 0 X X 0 X 0 X 0 0 0 X 0 X X 0 0 0 X 0 X X

generates a code of length 56 over Z2[X]/(X^2) who´s minimum homogenous weight is 52.

Homogenous weight enumerator: w(x)=1x^0+216x^52+164x^56+58x^60+49x^64+22x^68+2x^72

The gray image is a linear code over GF(2) with n=112, k=9 and d=52.
As d=52 is an upper bound for linear (112,9,2)-codes, this code is optimal over Z2[X]/(X^2) for dimension 9.
This code was found by an older version of Heurico in 0 seconds.