The generator matrix

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

generates a code of length 57 over Z2[X]/(X^3) who´s minimum homogenous weight is 47.

Homogenous weight enumerator: w(x)=1x^0+58x^47+215x^48+398x^49+660x^50+1124x^51+1518x^52+2010x^53+2543x^54+2770x^55+3084x^56+3652x^57+3569x^58+2898x^59+2527x^60+1956x^61+1454x^62+1032x^63+520x^64+334x^65+210x^66+114x^67+66x^68+34x^69+11x^70+4x^71+4x^72+1x^74+1x^76

The gray image is a linear code over GF(2) with n=228, k=15 and d=94.
This code was found by Heurico 1.16 in 37.8 seconds.