The generator matrix

 1  0  1  1 X^2  1  1  1 X^2+X  1  1  0 X^3+X  1  1  1  1 X^2 X^3+X^2+X  1  X  1  1  1  X  1  1 X^2 X^3  X X^3+X X^3 X^3  1  1 X^3  1  X  1  1  1  1  1  1  1  X  1  0 X^2+X  1  X  1
 0  1  1 X^2+X  1 X^2+X+1 X^2 X^3+1  1 X+1 X^3+X^2+X  1  1  0 X^3+X^2+1 X^3 X^3+1  1  1 X^3+X^2+1  1 X^2+X+1 X^3+X^2  X  1  X X+1  1  1  1  1  1  1 X^2+X X^3+X^2+X+1  1 X+1  1 X^2+X X^3+1  X X^3+X^2 X^2+X+1 X^3 X^3+1 X^2  1 X^3+X^2  1 X^3+X X^2+X X^3
 0  0  X  0 X^3+X  X X^3+X X^3  0 X^3 X^3+X X^3+X^2+X X^2 X^3+X^2 X^3+X^2 X^3+X^2+X X^3+X^2+X X^2+X X^3+X^2  X  X X^3+X^2  0 X^3+X^2+X  0 X^3+X^2 X^3+X^2+X  X X^3+X^2 X^3+X^2+X X^3+X^2+X X^3 X^3+X^2 X^3+X^2+X X^3 X^3+X X^3+X X^3+X X^3  0 X^3+X X^2+X X^3+X^2  X X^2+X  X X^2  X X^3+X^2 X^2+X X^2+X  0
 0  0  0 X^3  0 X^3 X^3 X^3 X^3  0  0 X^3 X^3  0 X^3 X^3  0  0  0 X^3 X^3  0 X^3  0  0 X^3 X^3 X^3 X^3  0 X^3 X^3  0 X^3 X^3 X^3  0  0  0  0 X^3  0 X^3  0 X^3 X^3  0  0 X^3 X^3  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+193x^48+478x^49+634x^50+600x^51+547x^52+564x^53+415x^54+304x^55+174x^56+78x^57+65x^58+24x^59+12x^60+5x^62+1x^66+1x^68

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 0.265 seconds.