The generator matrix

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

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+14x^54+24x^55+17x^56+144x^57+17x^58+24x^59+14x^60+1x^114

The gray image is a linear code over GF(2) with n=228, k=8 and d=108.
This code was found by Heurico 1.16 in 0.0962 seconds.