The generator matrix

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

generates a code of length 52 over Z2[X]/(X^4) who´s minimum homogenous weight is 45.

Homogenous weight enumerator: w(x)=1x^0+284x^45+1345x^46+3432x^47+6408x^48+10400x^49+14217x^50+19156x^51+20383x^52+19392x^53+14899x^54+10288x^55+5819x^56+3056x^57+1255x^58+500x^59+151x^60+52x^61+26x^62+4x^64+2x^68+2x^70

The gray image is a linear code over GF(2) with n=416, k=17 and d=180.
This code was found by Heurico 1.16 in 114 seconds.