The generator matrix

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

generates a code of length 57 over Z2[X]/(X^3) who´s minimum homogenous weight is 54.

Homogenous weight enumerator: w(x)=1x^0+58x^54+144x^55+80x^56+50x^57+32x^58+60x^59+18x^60+18x^61+18x^62+16x^63+12x^64+3x^66+1x^68+1x^70

The gray image is a linear code over GF(2) with n=228, k=9 and d=108.
This code was found by Heurico 1.11 in 0.047 seconds.