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  X  X  X  1  1  1  0 X^2  1  1  0  1  X  X  1  1  X  1 X^2  1  0  1 X^2 X^2  X  1  X  1  X  1
 0  X  0  0  0  X X^2+X  X  0 X^2 X^2  0  X X^2+X  X X^2+X X^2+X  0 X^2+X X^2+X X^2+X X^2  0  0  0  X X^2+X X^2  0 X^2+X X^2+X  0 X^2+X  X  X X^2 X^2+X  X  X X^2 X^2 X^2 X^2 X^2+X X^2+X  X X^2+X X^2  0 X^2  0 X^2+X X^2  X X^2  0 X^2
 0  0  X  0  X  X X^2+X  0  0  0 X^2+X X^2+X  X  X X^2  0  X  0 X^2  0 X^2+X X^2+X X^2 X^2+X X^2  X  0  X X^2+X X^2  0 X^2  0 X^2  X  X  0  X  X X^2  0 X^2 X^2+X  X  0  0 X^2+X  X X^2  X  X  0  X X^2+X  0  X  0
 0  0  0  X  X  0 X^2+X  X X^2 X^2+X  X X^2 X^2  X  X X^2  0 X^2 X^2+X  0  X X^2+X  X X^2  X  0  X X^2  0  0  X X^2  X  0 X^2  0  0 X^2+X  X X^2+X  X X^2 X^2+X  X  0 X^2  X X^2  X  X X^2+X X^2  0  0  X  X  X
 0  0  0  0 X^2  0  0  0 X^2  0  0  0  0  0  0 X^2 X^2 X^2 X^2 X^2  0  0 X^2 X^2 X^2 X^2  0 X^2 X^2 X^2  0 X^2 X^2  0 X^2 X^2 X^2 X^2 X^2 X^2  0  0 X^2  0  0 X^2 X^2 X^2 X^2  0  0  0 X^2 X^2 X^2  0  0
 0  0  0  0  0 X^2  0 X^2  0  0 X^2 X^2  0 X^2 X^2  0  0 X^2  0 X^2  0  0  0 X^2 X^2  0  0  0 X^2 X^2  0 X^2 X^2  0  0 X^2  0 X^2  0  0  0 X^2  0 X^2 X^2  0 X^2 X^2  0  0  0 X^2  0 X^2  0 X^2  0
 0  0  0  0  0  0 X^2 X^2 X^2 X^2  0  0 X^2  0  0  0  0 X^2  0 X^2  0  0  0 X^2 X^2 X^2 X^2  0  0 X^2  0  0 X^2 X^2  0  0 X^2 X^2  0  0 X^2  0 X^2 X^2  0  0  0 X^2 X^2  0 X^2 X^2  0 X^2 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+35x^48+74x^49+99x^50+164x^51+221x^52+246x^53+269x^54+374x^55+439x^56+376x^57+411x^58+362x^59+235x^60+246x^61+187x^62+94x^63+69x^64+68x^65+43x^66+26x^67+20x^68+12x^69+12x^70+4x^71+4x^72+2x^73+2x^74+1x^82

The gray image is a linear code over GF(2) with n=228, k=12 and d=96.
This code was found by Heurico 1.16 in 1.07 seconds.