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

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+83x^46+4x^47+213x^48+40x^49+233x^50+120x^51+287x^52+180x^53+263x^54+132x^55+189x^56+32x^57+131x^58+59x^60+4x^61+50x^62+16x^64+8x^66+2x^68+1x^80

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 0.303 seconds.