The generator matrix

 1  0  1  1  1 X^2+X  1  1 X^2  1  1  X  1  1  0  1  1 X^2+X  1  1 X^2  1  1  X  1  1  0  1  1 X^2+X  1  1  1  1 X^2  X  X  X  0  X  X X^2  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1
 0  1 X+1 X^2+X X^2+1  1 X^2 X^2+X+1  1  X  1  1  0 X+1  1 X^2+X X^2+1  1 X^2 X^2+X+1  1  X  1  1  0 X+1  1 X^2+X X^2+1  1 X^2  X X^2+X+1  1  1  1  0 X^2+X  X X^2  X  X  0 X+1 X^2 X^2+X+1 X^2+X  X X^2+1  1  0 X^2 X^2+X  X  0 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+7x^56+40x^57+4x^58+8x^59+2x^62+1x^70+1x^78

The gray image is a linear code over GF(2) with n=228, k=6 and d=112.
This code was found by Heurico 1.16 in 0.0451 seconds.