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  X  X  X X^3  X  X  X X^3  1  1
 0 X^3+X^2  0 X^3+X^2  0 X^3+X^2  0 X^3+X^2  0 X^3+X^2  0 X^3+X^2  0 X^3+X^2 X^3 X^2 X^3 X^2 X^3 X^2 X^3 X^2 X^3 X^2  0 X^3+X^2 X^3 X^2 X^3 X^2 X^3 X^2 X^3+X^2 X^3+X^2 X^3+X^2 X^2 X^3+X^2  0 X^3+X^2  0  0 X^3 X^3+X^2 X^2  0 X^3  0 X^3  0 X^3  0  0
 0  0 X^3  0  0  0 X^3  0  0 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 X^3 X^3  0  0 X^3 X^3  0  0  0  0  0  0 X^3 X^3 X^3  0 X^3  0 X^3 X^3  0 X^3 X^3 X^3  0 X^3  0  0
 0  0  0 X^3  0  0  0 X^3 X^3 X^3 X^3 X^3 X^3  0 X^3  0  0  0  0 X^3 X^3 X^3 X^3  0 X^3  0  0 X^3 X^3 X^3  0  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  0 X^3  0  0
 0  0  0  0 X^3 X^3 X^3 X^3 X^3  0  0 X^3  0 X^3 X^3  0  0 X^3 X^3 X^3  0  0 X^3  0 X^3  0  0 X^3  0  0 X^3 X^3  0 X^3 X^3  0  0  0 X^3 X^3  0 X^3 X^3  0  0  0 X^3 X^3  0  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+21x^48+242x^50+29x^52+176x^54+10x^56+28x^58+2x^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 0.109 seconds.