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

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+54x^49+112x^50+214x^51+284x^52+192x^53+112x^54+40x^55+2x^56+10x^57+2x^59+1x^96

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 0.156 seconds.