The generator matrix

 1  0  1  1  1 X^2+X  1  1  0  1 X^2+X  1  1  1  1  0  1 X^2+X  1  1  1  0  1  1 X^2+X  1  1 X^2  1  1  X  1  1  1  1  1  1  1  1  1  1  1 X^2+X  1  1  1  0  1  0  X X^2  1  1  X X^2  1  1
 0  1 X+1 X^2+X  1  1  0 X+1  1 X^2+X  1 X^2+1 X^2+1 X+1  0  1 X^2+X  1 X+1 X^2+1  0  1 X^2+1 X^2+X  1 X^2+X+1 X^2  1 X+1  X  1 X^2+1 X+1 X^2+X+1 X^2+1  1 X^2+1 X+1  1 X^2+X+1 X+1  0  1 X^2+1  1 X^2+X  1  X  1  0  X X^2+X+1 X^2  1  1  0 X+1
 0  0 X^2  0  0  0  0  0 X^2 X^2  0 X^2 X^2  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 X^2 X^2  0 X^2 X^2 X^2  0 X^2  0 X^2 X^2 X^2 X^2 X^2  0  0  0  0 X^2 X^2 X^2  0 X^2  0 X^2  0 X^2  0
 0  0  0 X^2  0  0  0  0 X^2 X^2 X^2  0  0 X^2 X^2 X^2 X^2 X^2 X^2 X^2  0  0 X^2  0  0  0  0  0  0  0 X^2 X^2  0 X^2 X^2  0 X^2 X^2 X^2 X^2  0 X^2 X^2  0  0  0 X^2  0 X^2 X^2 X^2 X^2  0  0  0  0 X^2
 0  0  0  0 X^2  0  0 X^2  0  0  0 X^2 X^2 X^2  0  0  0  0 X^2 X^2  0  0 X^2  0  0 X^2  0  0 X^2  0  0 X^2 X^2  0 X^2 X^2  0 X^2  0 X^2  0  0  0  0  0 X^2 X^2 X^2 X^2 X^2 X^2  0 X^2 X^2 X^2 X^2  0
 0  0  0  0  0 X^2 X^2 X^2 X^2  0 X^2  0 X^2  0 X^2  0 X^2  0 X^2 X^2 X^2 X^2  0  0  0  0  0  0  0 X^2 X^2  0 X^2  0 X^2 X^2 X^2 X^2  0  0 X^2  0  0  0 X^2 X^2  0 X^2  0  0 X^2 X^2  0 X^2  0  0 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+67x^52+92x^53+146x^54+60x^55+121x^56+88x^57+110x^58+56x^59+113x^60+76x^61+62x^62+12x^63+15x^64+2x^66+3x^80

The gray image is a linear code over GF(2) with n=228, k=10 and d=104.
This code was found by Heurico 1.16 in 0.119 seconds.