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

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+68x^50+4x^51+220x^52+60x^53+272x^54+128x^55+234x^56+144x^57+288x^58+116x^59+219x^60+44x^61+102x^62+8x^63+60x^64+8x^65+26x^66+29x^68+10x^70+4x^72+2x^74+1x^88

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 0.316 seconds.