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

generates a code of length 53 over Z2[X]/(X^3) who´s minimum homogenous weight is 46.

Homogenous weight enumerator: w(x)=1x^0+95x^46+200x^48+32x^49+211x^50+128x^51+282x^52+192x^53+298x^54+128x^55+195x^56+32x^57+122x^58+68x^60+39x^62+19x^64+3x^66+2x^68+1x^88

The gray image is a linear code over GF(2) with n=212, k=11 and d=92.
This code was found by Heurico 1.16 in 0.314 seconds.