The generator matrix

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

generates a code of length 57 over Z2[X]/(X^3) who´s minimum homogenous weight is 51.

Homogenous weight enumerator: w(x)=1x^0+40x^51+208x^52+142x^53+176x^54+176x^55+279x^56+86x^57+207x^58+182x^59+246x^60+78x^61+123x^62+42x^63+31x^64+10x^65+2x^67+2x^68+4x^69+4x^70+6x^71+1x^72+1x^74+1x^78

The gray image is a linear code over GF(2) with n=228, k=11 and d=102.
This code was found by Heurico 1.16 in 0.274 seconds.