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

generates a code of length 57 over Z2[X]/(X^4) who´s minimum homogenous weight is 50.

Homogenous weight enumerator: w(x)=1x^0+32x^50+76x^52+32x^53+154x^54+128x^55+530x^56+192x^57+506x^58+128x^59+136x^60+32x^61+50x^62+18x^64+22x^66+4x^68+4x^70+2x^72+1x^96

The gray image is a linear code over GF(2) with n=456, k=11 and d=200.
This code was found by Heurico 1.16 in 0.266 seconds.