The generator matrix

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

generates a code of length 57 over Z2[X]/(X^3) who´s minimum homogenous weight is 50.

Homogenous weight enumerator: w(x)=1x^0+34x^50+36x^51+153x^52+136x^53+217x^54+156x^55+223x^56+120x^57+279x^58+156x^59+227x^60+120x^61+90x^62+36x^63+30x^64+8x^65+14x^66+3x^68+3x^70+1x^72+1x^74+1x^76+2x^78+1x^80

The gray image is a linear code over GF(2) with n=228, k=11 and d=100.
This code was found by Heurico 1.16 in 0.256 seconds.