The generator matrix

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

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+39x^48+76x^49+180x^50+312x^51+385x^52+452x^53+628x^54+854x^55+867x^56+788x^57+791x^58+770x^59+615x^60+506x^61+384x^62+212x^63+117x^64+86x^65+41x^66+20x^67+20x^68+10x^69+23x^70+6x^71+4x^72+2x^73+2x^75+1x^78

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 3.63 seconds.