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.