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

generates a code of length 57 over Z2[X]/(X^3) who´s minimum homogenous weight is 49.

Homogenous weight enumerator: w(x)=1x^0+76x^49+117x^50+168x^51+236x^52+286x^53+333x^54+372x^55+367x^56+334x^57+385x^58+324x^59+313x^60+232x^61+137x^62+124x^63+73x^64+84x^65+46x^66+36x^67+29x^68+10x^69+6x^70+2x^72+2x^73+2x^76+1x^80

The gray image is a linear code over GF(2) with n=228, k=12 and d=98.
This code was found by Heurico 1.16 in 38.4 seconds.