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.