The generator matrix

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

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+68x^48+88x^50+112x^51+285x^52+224x^53+252x^54+400x^55+382x^56+576x^57+276x^58+400x^59+327x^60+224x^61+132x^62+112x^63+185x^64+20x^66+19x^68+2x^72+9x^76+2x^80

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 0.805 seconds.