The generator matrix

 1  0  1  1  1 X^2+X  1  1 X^3+X^2  1  1 X^3+X  1  1  0  1  1 X^2+X  1  1 X^3+X^2  1  1 X^3+X  1  1  0  1 X^2+X  1  1 X^3+X^2 X^2+X X^3+X X^3  1  1  1 X^2+X X^3+X^2+X  0  0 X^3+X^2  0  1 X^3 X^3+X  1  1  1  1  1  1  1  1 X^3+X  1
 0  1 X+1 X^2+X X^2+1  1 X^3+X^2 X^3+X^2+X+1  1 X^3+X X^3+1  1  0 X+1  1 X^2+X X^2+1  1 X^3+X^2 X^3+X^2+X+1  1 X^3+X X^3+1  1 X^3+X X+1  1  0  1 X^3+X^2+X+1 X^2+1  1  1  1  1 X^2+1 X+1 X^3+1  1  1  1  1  1  1 X^2+1  1  1 X+1 X^3+X^2+1 X^3+X^2+X+1 X^3+X^2 X^3+X+1 X^3+X+1 X^2+X X+1  1  0
 0  0 X^3  0  0  0  0  0 X^3  0 X^3 X^3 X^3  0 X^3 X^3  0 X^3  0  0  0 X^3 X^3  0 X^3 X^3  0 X^3  0  0 X^3 X^3 X^3  0 X^3  0 X^3  0 X^3 X^3 X^3  0  0  0  0 X^3  0  0 X^3 X^3  0 X^3  0  0 X^3  0  0
 0  0  0 X^3  0  0  0  0 X^3 X^3  0 X^3 X^3 X^3  0 X^3 X^3  0  0  0  0 X^3  0  0 X^3  0 X^3 X^3  0 X^3  0  0 X^3  0 X^3 X^3  0  0  0  0 X^3  0 X^3  0 X^3 X^3 X^3  0  0 X^3 X^3 X^3 X^3  0 X^3 X^3 X^3
 0  0  0  0 X^3  0  0 X^3  0 X^3 X^3 X^3  0 X^3 X^3 X^3  0  0 X^3  0 X^3 X^3  0 X^3  0 X^3 X^3 X^3  0  0 X^3  0 X^3 X^3  0 X^3  0  0 X^3 X^3 X^3 X^3  0  0 X^3 X^3  0 X^3  0  0  0  0  0  0  0 X^3 X^3
 0  0  0  0  0 X^3 X^3 X^3 X^3  0  0 X^3  0  0 X^3 X^3 X^3  0 X^3  0  0  0 X^3 X^3  0  0 X^3 X^3  0 X^3 X^3  0  0  0  0 X^3 X^3 X^3 X^3  0  0 X^3  0 X^3  0 X^3 X^3  0  0  0 X^3 X^3  0 X^3  0  0  0

generates a code of length 57 over Z2[X]/(X^4) who´s minimum homogenous weight is 52.

Homogenous weight enumerator: w(x)=1x^0+80x^52+312x^53+284x^54+480x^55+604x^56+592x^57+584x^58+480x^59+295x^60+312x^61+60x^62+4x^64+5x^68+2x^72+1x^88

The gray image is a linear code over GF(2) with n=456, k=12 and d=208.
This code was found by Heurico 1.16 in 0.281 seconds.