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

generates a code of length 57 over Z2[X]/(X^3) who´s minimum homogenous weight is 55.

Homogenous weight enumerator: w(x)=1x^0+240x^55+60x^56+32x^57+60x^58+48x^59+64x^63+3x^64+4x^66

The gray image is a linear code over GF(2) with n=228, k=9 and d=110.
This code was found by Heurico 1.16 in 27.3 seconds.