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

generates a code of length 57 over Z2[X]/(X^3) who´s minimum homogenous weight is 48.

Homogenous weight enumerator: w(x)=1x^0+177x^48+454x^50+72x^51+617x^52+172x^53+848x^54+472x^55+1052x^56+596x^57+960x^58+504x^59+864x^60+180x^61+592x^62+40x^63+284x^64+12x^65+178x^66+70x^68+40x^70+6x^72+1x^84

The gray image is a linear code over GF(2) with n=228, k=13 and d=96.
This code was found by Heurico 1.16 in 4.65 seconds.