The generator matrix

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

generates a code of length 53 over Z2[X]/(X^4) who´s minimum homogenous weight is 49.

Homogenous weight enumerator: w(x)=1x^0+408x^49+893x^50+1288x^51+1290x^52+1276x^53+848x^54+808x^55+495x^56+452x^57+257x^58+96x^59+52x^60+20x^61+2x^62+2x^64+4x^65

The gray image is a linear code over GF(2) with n=424, k=13 and d=196.
This code was found by Heurico 1.16 in 4.56 seconds.