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  X X^2  X  1  X  1  1  1  X  1  1  X  1  1  1 X^2  X  1  X  1  1 X^2  X  0  1
 0  X  0  0  0  X X^2+X  X X^2 X^2  X  0  0  X  X X^2+X  0  0 X^2+X  X X^2  X X^2+X  X X^2  0 X^2 X^2 X^2+X  0  X X^2+X  X  X  X X^2  X  0 X^2+X X^2  X X^2+X  0 X^2+X  X  X X^2+X  X  0 X^2+X X^2+X  X  X  0 X^2  0 X^2
 0  0  X  0  X  X  X  0 X^2  0 X^2+X  X X^2+X  0 X^2+X  0 X^2 X^2+X X^2 X^2+X  0 X^2  X  0 X^2+X X^2+X  X X^2  X X^2  0 X^2+X  X X^2+X X^2  0 X^2  X X^2+X X^2+X X^2+X X^2 X^2+X  0  0 X^2+X  0  X  X  X  0 X^2 X^2  X  X  0 X^2
 0  0  0  X  X  0  X X^2+X  0  X X^2  X X^2 X^2+X  X  0 X^2  X  X  0 X^2+X X^2 X^2+X X^2+X  0  0 X^2+X  X  X  0  0  0 X^2 X^2 X^2+X  X  X X^2+X  X X^2+X  0  X  0 X^2 X^2 X^2  0  X  X X^2 X^2  0 X^2+X X^2+X  0  X  X
 0  0  0  0 X^2  0  0  0 X^2 X^2 X^2 X^2  0 X^2  0 X^2 X^2  0  0  0 X^2  0 X^2 X^2 X^2 X^2  0  0 X^2  0 X^2 X^2  0  0  0 X^2  0  0 X^2  0 X^2 X^2  0 X^2 X^2 X^2  0 X^2 X^2  0  0  0  0 X^2 X^2 X^2 X^2
 0  0  0  0  0 X^2  0 X^2  0  0  0 X^2 X^2  0 X^2  0 X^2 X^2  0  0 X^2 X^2 X^2 X^2  0 X^2  0 X^2  0 X^2 X^2 X^2  0 X^2 X^2 X^2  0  0 X^2  0 X^2  0  0  0 X^2 X^2 X^2  0  0  0 X^2  0 X^2 X^2 X^2 X^2 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+44x^50+102x^51+139x^52+116x^53+139x^54+200x^55+207x^56+218x^57+222x^58+210x^59+113x^60+82x^61+77x^62+46x^63+36x^64+30x^65+25x^66+16x^67+16x^68+2x^69+4x^70+2x^71+1x^90

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 0.347 seconds.