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

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+29x^46+74x^47+121x^48+152x^49+173x^50+236x^51+211x^52+184x^53+225x^54+180x^55+128x^56+94x^57+56x^58+52x^59+41x^60+28x^61+24x^62+18x^63+8x^64+6x^65+4x^66+2x^68+1x^82

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 0.277 seconds.