The generator matrix

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

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+272x^47+1024x^48+1482x^49+1974x^50+2446x^51+2592x^52+2084x^53+1938x^54+1186x^55+707x^56+378x^57+175x^58+42x^59+24x^60+40x^61+8x^62+6x^63+2x^64+1x^66+2x^68

The gray image is a linear code over GF(2) with n=416, k=14 and d=188.
This code was found by Heurico 1.16 in 2.75 seconds.