The generator matrix

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

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+80x^54+84x^55+100x^56+48x^57+68x^58+40x^59+47x^60+16x^61+18x^62+4x^63+2x^68+2x^70+1x^76+1x^88

The gray image is a linear code over GF(2) with n=228, k=9 and d=108.
This code was found by Heurico 1.16 in 0.104 seconds.