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

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+46x^49+79x^50+160x^51+451x^52+170x^53+72x^54+36x^55+4x^56+4x^57+1x^102

The gray image is a linear code over GF(2) with n=416, k=10 and d=196.
This code was found by Heurico 1.16 in 0.078 seconds.