The generator matrix

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

generates a code of length 52 over Z2[X]/(X^4) who´s minimum homogenous weight is 47.

Homogenous weight enumerator: w(x)=1x^0+88x^47+212x^48+396x^49+477x^50+584x^51+575x^52+716x^53+450x^54+264x^55+167x^56+100x^57+29x^58+24x^59+5x^60+4x^61+1x^62+1x^70+2x^74

The gray image is a linear code over GF(2) with n=416, k=12 and d=188.
This code was found by Heurico 1.16 in 6.58 seconds.