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  X  1  1  1  1  1  1  1  1  1  1 X^2  1 X^2  1  1  1  X X^2
 0 X^3+X^2  0 X^2  0  0 X^2 X^2 X^3 X^3 X^2 X^3+X^2  0 X^3 X^2 X^2  0 X^3  0 X^3+X^2 X^2  0 X^2 X^2 X^3+X^2 X^3 X^2  0 X^2  0 X^3 X^2 X^3+X^2 X^3+X^2  0  0 X^3+X^2 X^3+X^2 X^3+X^2  0 X^3+X^2 X^3+X^2 X^2 X^3 X^3+X^2 X^2 X^3  0 X^2  0 X^3 X^3+X^2 X^3+X^2 X^2 X^3 X^3+X^2 X^2
 0  0 X^3+X^2 X^2  0 X^3+X^2 X^3+X^2  0 X^3 X^2 X^2  0 X^3 X^2 X^3+X^2  0  0 X^2 X^2  0  0 X^3 X^2 X^2 X^3 X^2 X^3 X^2 X^3+X^2 X^3  0 X^3+X^2 X^3+X^2 X^3+X^2  0  0 X^3+X^2 X^3+X^2 X^3 X^3  0 X^3 X^3 X^2 X^2 X^3+X^2 X^3 X^3+X^2 X^2 X^3+X^2 X^3+X^2 X^3 X^2 X^3+X^2  0 X^3 X^3+X^2
 0  0  0 X^3  0  0 X^3  0  0 X^3  0 X^3 X^3 X^3  0 X^3  0  0 X^3  0 X^3 X^3  0 X^3 X^3 X^3  0  0 X^3 X^3 X^3  0  0  0 X^3 X^3 X^3 X^3  0  0 X^3  0  0  0  0 X^3  0  0 X^3  0  0 X^3  0 X^3  0  0 X^3
 0  0  0  0 X^3  0  0  0  0  0  0  0 X^3  0  0  0 X^3 X^3 X^3 X^3 X^3 X^3 X^3 X^3 X^3 X^3 X^3 X^3 X^3  0  0 X^3  0  0 X^3 X^3 X^3 X^3 X^3  0 X^3 X^3 X^3  0 X^3  0 X^3 X^3  0 X^3  0 X^3  0 X^3 X^3 X^3  0
 0  0  0  0  0 X^3 X^3 X^3 X^3 X^3  0 X^3  0  0 X^3  0 X^3 X^3  0 X^3  0 X^3 X^3  0 X^3 X^3  0  0 X^3 X^3  0  0  0 X^3  0 X^3  0 X^3  0  0  0 X^3 X^3  0 X^3  0 X^3  0 X^3 X^3 X^3  0 X^3  0  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+153x^52+64x^54+192x^55+385x^56+640x^57+128x^58+192x^59+218x^60+61x^64+13x^68+1x^104

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 1.64 seconds.