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

generates a code of length 52 over Z2[X]/(X^3) who´s minimum homogenous weight is 44.

Homogenous weight enumerator: w(x)=1x^0+61x^44+116x^46+299x^48+326x^50+474x^52+350x^54+233x^56+98x^58+63x^60+6x^62+15x^64+2x^68+3x^72+1x^80

The gray image is a linear code over GF(2) with n=208, k=11 and d=88.
This code was found by Heurico 1.16 in 0.329 seconds.