The generator matrix

 1  0  0  0  1  1  1  0  1  X X^2  1  0  1  1  0  1 X^2+X  1 X^2  1  X  1  X  0  1  1  1 X^2  1  1 X^2+X  1 X^2+X  1  1 X^2+X  0 X^2  1  1  0  0  1  1  1  X  0  1 X^2+X  1  1 X^2+X  0  1  1  1
 0  1  0  0  0  1  1  1 X^2 X^2+X  1  1  1  X X^2+1  X  0  1  1  1 X+1  1 X^2+X+1  1 X^2+X X^2+1 X^2 X^2+X  X  X  X  1 X^2  0  1 X^2+1  1  1  0 X^2+X X+1  1  X  1 X^2 X^2+X+1  1 X^2+X X^2+X  1 X^2+X+1  0 X^2+X X^2+X X^2+X+1 X^2+X  0
 0  0  1  0  1  1 X^2 X^2+1 X^2+X+1  1 X^2+X  X X+1  0 X^2+X+1  1 X^2+X+1 X^2+X X^2 X^2+1  0  1 X^2+X+1  X  1 X^2+1 X^2 X+1 X^2  X X^2  0  1  1 X^2+1 X^2  X  1  1  1  1 X+1  X X^2+X X+1  0 X^2+X  1 X^2  0  X  0 X^2  1  1  1 X+1
 0  0  0  1  1  0 X^2+1  1 X^2  1 X^2+1  X X^2 X+1 X^2+X+1  0  1 X^2+1 X^2 X^2+X+1  1 X^2+X X^2+X+1 X^2+X X^2+X+1 X^2+X  1 X^2  1 X^2 X+1 X^2+1 X+1  1  0  1  X X^2+X+1  X X^2+1  0  X  1 X^2+X  0 X^2+X+1 X^2+X+1 X^2 X^2+X X^2+X+1  X X^2+X+1  1 X^2+1  X X^2+X X^2+X
 0  0  0  0  X  0  0  0  0  0  0  0  0  0 X^2 X^2 X^2 X^2 X^2 X^2  0  0 X^2  0  0 X^2 X^2+X X^2+X  X  X  X X^2+X  X  X X^2+X X^2+X  X  X  X X^2  X X^2 X^2+X X^2+X  X X^2 X^2+X X^2+X X^2+X  X  X X^2+X  0 X^2+X X^2  X  X
 0  0  0  0  0 X^2  0 X^2 X^2 X^2  0  0 X^2  0 X^2 X^2 X^2  0 X^2  0 X^2  0  0 X^2  0 X^2 X^2  0  0 X^2  0 X^2 X^2 X^2 X^2  0 X^2 X^2 X^2  0 X^2  0  0 X^2 X^2 X^2  0  0  0 X^2 X^2  0 X^2 X^2  0  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+142x^48+458x^49+726x^50+1276x^51+1604x^52+1780x^53+2513x^54+2994x^55+3173x^56+3314x^57+3305x^58+2966x^59+2594x^60+2130x^61+1491x^62+1010x^63+571x^64+360x^65+175x^66+70x^67+70x^68+18x^69+12x^70+4x^71+5x^72+4x^73+2x^74

The gray image is a linear code over GF(2) with n=228, k=15 and d=96.
This code was found by Heurico 1.16 in 35.3 seconds.