The generator matrix

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

generates a code of length 53 over Z2[X]/(X^4) who´s minimum homogenous weight is 51.

Homogenous weight enumerator: w(x)=1x^0+316x^51+149x^52+184x^53+77x^54+220x^55+25x^56+48x^57+2x^58+1x^70+1x^76

The gray image is a linear code over GF(2) with n=424, k=10 and d=204.
This code was found by Heurico 1.16 in 9.39 seconds.