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

generates a code of length 52 over Z2[X]/(X^4) who´s minimum homogenous weight is 49.

Homogenous weight enumerator: w(x)=1x^0+218x^49+435x^50+358x^51+268x^52+220x^53+279x^54+114x^55+50x^56+62x^57+20x^58+20x^59+2x^66+1x^68

The gray image is a linear code over GF(2) with n=416, k=11 and d=196.
This code was found by Heurico 1.16 in 0.625 seconds.