The generator matrix

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

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+212x^50+168x^51+718x^52+288x^53+1121x^54+396x^55+1106x^56+376x^57+1139x^58+388x^59+959x^60+256x^61+525x^62+132x^63+231x^64+40x^65+87x^66+4x^67+22x^68+18x^70+2x^72+2x^74+1x^76

The gray image is a linear code over GF(2) with n=228, k=13 and d=100.
This code was found by Heurico 1.16 in 3.06 seconds.