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

generates a code of length 52 over Z2[X]/(X^4) who´s minimum homogenous weight is 48.

Homogenous weight enumerator: w(x)=1x^0+25x^48+42x^50+128x^51+153x^52+128x^53+6x^56+20x^58+6x^60+2x^66+1x^68

The gray image is a linear code over GF(2) with n=416, k=9 and d=192.
This code was found by Heurico 1.16 in 0.078 seconds.