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

generates a code of length 52 over Z2[X]/(X^3) who´s minimum homogenous weight is 46.

Homogenous weight enumerator: w(x)=1x^0+172x^46+28x^47+244x^48+76x^49+246x^50+152x^51+294x^52+152x^53+226x^54+76x^55+168x^56+28x^57+100x^58+44x^60+22x^62+14x^64+2x^66+2x^68+1x^80

The gray image is a linear code over GF(2) with n=208, k=11 and d=92.
This code was found by Heurico 1.16 in 17.6 seconds.