The generator matrix

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

generates a code of length 57 over Z2[X]/(X^3) who´s minimum homogenous weight is 56.

Homogenous weight enumerator: w(x)=1x^0+156x^56+64x^58+32x^60+1x^64+2x^80

The gray image is a linear code over GF(2) with n=228, k=8 and d=112.
As d=112 is an upper bound for linear (228,8,2)-codes, this code is optimal over Z2[X]/(X^3) for dimension 8.
This code was found by Heurico 1.16 in 0.0716 seconds.