The generator matrix

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

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+304x^48+384x^49+512x^50+640x^51+438x^52+640x^53+512x^54+384x^55+256x^56+18x^60+5x^64+2x^72

The gray image is a linear code over GF(2) with n=416, k=12 and d=192.
This code was found by Heurico 1.16 in 0.391 seconds.