The generator matrix

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

generates a code of length 57 over Z2[X]/(X^3) who´s minimum homogenous weight is 52.

Homogenous weight enumerator: w(x)=1x^0+118x^52+192x^53+265x^54+232x^55+268x^56+150x^57+211x^58+150x^59+133x^60+92x^61+66x^62+56x^63+45x^64+12x^65+24x^66+10x^67+19x^68+1x^70+2x^73+1x^74

The gray image is a linear code over GF(2) with n=228, k=11 and d=104.
This code was found by Heurico 1.16 in 0.211 seconds.