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 X^2  0  X  0  X X^2  0  X  X  1  0  0 X^2  1  1  1  1  X  1  0  X  1  1
 0  X  0  0  0  0  0  0  0 X^2+X  X  X  X  X X^2 X^2  0  X X^2 X^2+X  X  0 X^2 X^2  X  0  X X^2+X X^2 X^2+X  0  0  X  X  X X^2  0 X^2 X^2+X  X  0  X X^2  0  0  X X^2  X X^2  0 X^2+X X^2+X X^2+X X^2 X^2+X X^2 X^2+X
 0  0  X  0  0  0  X X^2+X  X X^2  X X^2+X  0  0  X X^2+X X^2+X X^2+X  0 X^2  X X^2+X X^2+X X^2+X  X X^2 X^2+X  X X^2+X  0  0  X  X X^2  0  0 X^2  0 X^2+X X^2+X  X X^2 X^2+X  0  X X^2 X^2 X^2+X X^2  0  X X^2+X X^2  X X^2  X X^2
 0  0  0  X  0  X  X  X  0 X^2+X X^2  X X^2+X  0  X X^2+X  0  0 X^2+X  X X^2  X X^2  0 X^2  0  X  X  0  X  0 X^2+X X^2+X  0 X^2  0 X^2  X X^2 X^2 X^2+X  0  X X^2+X  X  X  X X^2+X X^2  0  0 X^2+X X^2 X^2 X^2+X  X  0
 0  0  0  0  X  X  0  X X^2+X  X  0  X X^2 X^2+X X^2+X  0  X X^2+X X^2 X^2  0 X^2+X  0  X  0  X X^2+X  0 X^2 X^2+X X^2 X^2+X X^2 X^2 X^2+X  X X^2+X X^2 X^2+X  0  X  X  0  0 X^2+X X^2+X X^2+X X^2+X  0  X  X X^2+X  X  0 X^2  X  X
 0  0  0  0  0 X^2  0  0  0  0  0  0  0 X^2 X^2 X^2 X^2 X^2 X^2  0 X^2  0 X^2  0 X^2 X^2 X^2  0  0 X^2 X^2 X^2 X^2 X^2  0  0  0 X^2  0 X^2 X^2 X^2  0  0  0 X^2  0  0  0 X^2  0  0 X^2  0  0  0  0
 0  0  0  0  0  0 X^2  0 X^2  0 X^2 X^2 X^2 X^2  0 X^2 X^2  0 X^2  0 X^2 X^2 X^2  0  0 X^2 X^2  0 X^2  0 X^2 X^2  0 X^2 X^2 X^2  0  0  0  0  0  0  0 X^2  0  0 X^2  0 X^2  0  0  0 X^2  0 X^2 X^2  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+198x^48+388x^50+60x^51+657x^52+216x^53+840x^54+436x^55+1065x^56+592x^57+1010x^58+484x^59+850x^60+216x^61+530x^62+44x^63+321x^64+146x^66+92x^68+30x^70+15x^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 4.81 seconds.