The generator matrix

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

generates a code of length 57 over Z2[X]/(X^3) who´s minimum homogenous weight is 51.

Homogenous weight enumerator: w(x)=1x^0+128x^51+248x^52+388x^53+362x^54+488x^55+352x^56+482x^57+333x^58+350x^59+236x^60+264x^61+138x^62+94x^63+76x^64+76x^65+25x^66+26x^67+14x^68+4x^69+6x^70+2x^71+1x^72+2x^73

The gray image is a linear code over GF(2) with n=228, k=12 and d=102.
This code was found by Heurico 1.16 in 0.925 seconds.