The generator matrix

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

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+114x^52+196x^53+253x^54+240x^55+295x^56+148x^57+180x^58+142x^59+157x^60+88x^61+72x^62+40x^63+40x^64+26x^65+29x^66+10x^67+9x^68+4x^69+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 1.11 in 0.109 seconds.