The generator matrix

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

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+90x^47+461x^48+986x^49+1509x^50+2240x^51+3029x^52+4170x^53+4683x^54+5980x^55+6152x^56+6654x^57+6128x^58+6330x^59+4966x^60+4308x^61+3034x^62+1980x^63+1252x^64+778x^65+367x^66+238x^67+135x^68+26x^69+23x^70+6x^71+2x^72+6x^73+2x^76

The gray image is a linear code over GF(2) with n=228, k=16 and d=94.
This code was found by Heurico 1.13 in 43.4 seconds.