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  1  1  1  1  1  1  1  1  1  1  1  1  1  1  X  1  1  X  1  1 X^2 X^2  1  1  X X^2  1  1 X^2
 0 X^3+X^2  0  0  0 X^2 X^3+X^2 X^2  0 X^3 X^3+X^2 X^3+X^2  0 X^3 X^3+X^2 X^3+X^2  0 X^3 X^3 X^3 X^3+X^2 X^3+X^2 X^2 X^3+X^2 X^2  0 X^2  0 X^3  0 X^3+X^2 X^3+X^2 X^2  0 X^3 X^2 X^3+X^2  0 X^3 X^3+X^2 X^3+X^2 X^2  0 X^2 X^3+X^2 X^3+X^2 X^3 X^3+X^2 X^3+X^2 X^3+X^2 X^2 X^3+X^2  0 X^2 X^2 X^3+X^2 X^3+X^2
 0  0 X^3+X^2  0 X^2 X^2 X^2 X^3  0 X^3 X^2 X^3+X^2 X^2 X^2 X^3 X^3  0 X^3+X^2 X^3+X^2  0  0  0 X^3+X^2 X^3+X^2 X^3+X^2 X^3 X^3  0 X^2 X^3+X^2  0 X^3+X^2 X^3+X^2 X^3  0 X^3+X^2 X^2 X^3  0 X^2 X^2  0 X^3  0 X^3  0 X^3+X^2 X^3 X^3 X^3 X^3+X^2 X^3+X^2 X^2 X^3+X^2 X^2 X^3 X^3+X^2
 0  0  0 X^3+X^2 X^2 X^3 X^3+X^2 X^3+X^2  0 X^3+X^2 X^3 X^3+X^2 X^2  0 X^3+X^2  0 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^3 X^3 X^2 X^3 X^3+X^2  0  0 X^3 X^3 X^3 X^3  0  0 X^2 X^3+X^2 X^2 X^2 X^3+X^2 X^2 X^3 X^3 X^3+X^2 X^3  0 X^3+X^2 X^3 X^2 X^3 X^3+X^2 X^2 X^3+X^2
 0  0  0  0 X^3 X^3 X^3 X^3 X^3 X^3  0  0  0 X^3  0 X^3 X^3 X^3 X^3  0 X^3 X^3  0 X^3  0 X^3  0  0  0  0  0 X^3  0  0  0 X^3 X^3 X^3 X^3  0  0  0  0  0 X^3 X^3  0 X^3  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+124x^52+32x^53+108x^54+192x^55+430x^56+320x^57+422x^58+192x^59+83x^60+32x^61+64x^62+24x^64+14x^66+8x^68+1x^72+1x^100

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 0.25 seconds.