The generator matrix

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

generates a code of length 53 over Z2[X]/(X^4) who´s minimum homogenous weight is 50.

Homogenous weight enumerator: w(x)=1x^0+279x^50+410x^51+270x^52+196x^53+245x^54+366x^55+234x^56+16x^57+12x^58+4x^59+4x^60+8x^62+2x^68+1x^76

The gray image is a linear code over GF(2) with n=424, k=11 and d=200.
This code was found by Heurico 1.16 in 0.609 seconds.