The generator matrix

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

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+463x^48+128x^49+544x^50+384x^51+1084x^52+384x^53+544x^54+128x^55+414x^56+12x^60+8x^64+2x^80

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 1.52 seconds.