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  0  1  1  X  1 X^3  1  X  1  X  1  1  1 X^3+X^2  1  0  X  X  X  1 X^3  1
 0  X  0  X X^3  0 X^2+X X^3+X^2+X  0 X^3 X^3+X X^3+X  0 X^3+X^2+X X^3+X^2  X X^3+X^2 X^2+X X^3+X^2+X X^3 X^3 X^2+X X^3+X X^3 X^2 X^2+X X^2 X^2+X X^3+X^2+X X^2+X X^3+X^2 X^3+X X^2 X^2 X^2  X X^3 X^3+X  X X^3  X  X X^2 X^3+X^2+X X^3+X^2+X X^2 X^3+X^2 X^2  X X^3+X X^3 X^3 X^3+X  X X^2  0 X^3
 0  0  X  X  0 X^3+X^2+X X^2+X X^3 X^2 X^3+X^2+X X^3+X^2+X X^2 X^3+X^2 X^2  X  X X^3+X^2+X X^3+X  X X^3+X X^3+X^2  0 X^3 X^3+X^2 X^2 X^2 X^3+X X^3+X  X X^3+X^2 X^3+X^2+X X^2+X X^3 X^3 X^3+X X^2 X^2+X X^3 X^3+X^2+X  0  0 X^3+X^2+X X^3+X X^3 X^3  0 X^3+X^2 X^3+X X^2+X  X  X  X  0  0  X X^2 X^2
 0  0  0 X^2 X^3+X^2 X^2 X^3 X^2 X^2  0 X^2 X^3+X^2  0  0 X^3+X^2 X^3 X^2 X^3+X^2 X^3 X^2 X^3 X^3 X^2 X^3+X^2 X^3 X^3 X^3 X^2  0 X^2 X^3  0  0 X^2  0 X^3+X^2 X^3+X^2 X^3 X^2 X^2  0 X^3+X^2 X^3+X^2 X^3+X^2 X^2 X^3+X^2 X^3+X^2 X^2  0 X^3 X^2 X^3  0 X^2 X^3+X^2  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+153x^52+226x^53+379x^54+492x^55+633x^56+592x^57+540x^58+356x^59+325x^60+150x^61+81x^62+64x^63+38x^64+40x^65+21x^66+2x^68+2x^74+1x^90

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 0.391 seconds.