The generator matrix

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

generates a code of length 52 over Z2[X]/(X^4) who´s minimum homogenous weight is 51.

Homogenous weight enumerator: w(x)=1x^0+32x^51+188x^52+32x^53+1x^64+2x^72

The gray image is a linear code over GF(2) with n=416, k=8 and d=204.
This code was found by Heurico 1.16 in 0.547 seconds.