The generator matrix

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

generates a code of length 52 over Z2[X]/(X^4) who´s minimum homogenous weight is 49.

Homogenous weight enumerator: w(x)=1x^0+564x^49+734x^50+726x^51+644x^52+424x^53+350x^54+236x^55+170x^56+148x^57+18x^58+78x^59+2x^62+1x^64

The gray image is a linear code over GF(2) with n=416, k=12 and d=196.
This code was found by Heurico 1.16 in 24.8 seconds.