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

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+27x^52+156x^53+45x^54+396x^55+66x^56+766x^57+54x^58+336x^59+25x^60+80x^61+25x^62+20x^63+7x^64+38x^65+3x^66+2x^68+1x^98

The gray image is a linear code over GF(2) with n=456, k=11 and d=208.
This code was found by Heurico 1.16 in 0.282 seconds.