The generator matrix

 1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  X  1 X^2  1  1  1  1  1  X  1  1  0  1  1  1  1  X  1  1  1  X  1  1 X^3 X^3  1 X^3 X^2  1
 0  X  0  X  0 X^3 X^2+X  X X^2 X^2+X X^2 X^3+X^2+X X^2 X^3+X^2 X^3+X X^3+X^2+X X^3+X X^2 X^3+X^2 X^3+X^2+X X^3+X^2+X X^3 X^2+X X^3+X X^2 X^2 X^2 X^3+X^2+X X^3 X^2 X^3+X X^3+X^2+X X^3+X^2  X  X  0 X^3+X X^2+X X^3+X X^2 X^3 X^3+X^2+X  0 X^2 X^2 X^3  X X^3+X^2 X^3+X^2+X  X  X  X
 0  0  X  X X^3+X^2 X^3+X^2+X X^2+X X^2 X^3+X^2 X^3  0 X^3+X^2  X X^2+X X^2+X  X X^3+X  X  0 X^3+X^2 X^3+X X^3+X^2+X X^2 X^3+X^2+X X^3+X  X X^3+X^2 X^3+X^2+X X^3 X^2  0 X^3+X^2 X^3+X X^2 X^3 X^3+X X^3+X^2+X X^3+X^2+X X^2+X X^3+X^2+X X^2 X^3+X^2+X X^2 X^3+X^2+X  0 X^3+X^2 X^2  X X^3+X X^2 X^3+X^2+X X^3+X^2
 0  0  0 X^3  0  0  0 X^3 X^3 X^3 X^3  0 X^3 X^3  0 X^3  0 X^3  0 X^3 X^3 X^3  0 X^3  0  0 X^3 X^3 X^3  0 X^3  0  0  0  0  0 X^3  0 X^3  0  0  0 X^3 X^3  0 X^3 X^3 X^3  0 X^3 X^3 X^3
 0  0  0  0 X^3 X^3  0  0  0 X^3 X^3 X^3  0 X^3 X^3 X^3  0 X^3  0 X^3  0  0  0  0 X^3  0 X^3 X^3  0 X^3  0  0  0 X^3 X^3 X^3 X^3 X^3  0 X^3  0  0 X^3  0 X^3  0 X^3 X^3  0  0 X^3 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+140x^47+216x^48+304x^49+464x^50+644x^51+739x^52+582x^53+440x^54+174x^55+122x^56+156x^57+40x^58+32x^59+24x^60+14x^61+2x^63+1x^64+1x^84

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 0.359 seconds.