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

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+18x^49+29x^50+24x^51+69x^52+256x^53+60x^54+23x^56+12x^57+3x^58+8x^59+3x^60+3x^62+2x^65+1x^70

The gray image is a linear code over GF(2) with n=424, k=9 and d=196.
This code was found by Heurico 1.16 in 1.69 seconds.