The generator matrix

 1  0  1  1  1 X^2  1  1  0  0  1  1  1  0  1  1  1  0  1  1  0  1  1 X^2  1  1 X^2+X  1  1  1  X  0  1  1  1  1  X  1  X  X  1  1 X^2  1 X^2+X  0  1  X  1  1  1  1  1
 0  1  1  0  1  1 X^2 X+1  1  1 X^2 X^2+X+1 X^2  1 X^2+1 X+1 X^2  1  X X+1  1  0  1  1 X^2+X X^2+X+1  1 X+1 X^2+1  0  1  1 X+1 X^2+X+1  X X^2+X+1  1 X^2+X+1  1  1  X X^2  1 X+1  1  1 X^2+1  1 X+1 X+1 X^2+X  0  0
 0  0  X  0  0  0  0 X^2 X^2+X  X X^2+X X^2+X X^2+X X^2  0  X X^2+X  X  X  0  0 X^2 X^2+X  X X^2+X  X X^2 X^2 X^2 X^2+X  0  X X^2 X^2 X^2 X^2 X^2+X  X X^2 X^2+X  X  0  X  X  X X^2+X X^2+X X^2  X X^2+X X^2 X^2  0
 0  0  0  X  0  0 X^2 X^2 X^2 X^2  0 X^2 X^2 X^2+X  X  X  X X^2+X  X X^2+X  X X^2+X X^2+X X^2+X X^2 X^2  0 X^2  X  X  0  X  X X^2  0  0  0  X  X  0 X^2+X  0  X X^2+X  0 X^2+X X^2  X X^2+X  0 X^2+X  X  0
 0  0  0  0  X X^2+X X^2+X X^2  X  0  0 X^2+X  X  X  X  X X^2  0 X^2+X  0 X^2 X^2+X X^2 X^2 X^2  0 X^2  0  0 X^2+X X^2+X X^2+X  X  X X^2  0  X  0 X^2  0 X^2+X  X X^2  X  X  X X^2+X X^2+X X^2 X^2 X^2+X  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+42x^46+150x^47+252x^48+286x^49+326x^50+400x^51+442x^52+442x^53+433x^54+366x^55+277x^56+240x^57+187x^58+120x^59+37x^60+18x^61+26x^62+16x^63+10x^64+6x^65+6x^66+4x^67+5x^68+3x^70+1x^74

The gray image is a linear code over GF(2) with n=212, k=12 and d=92.
This code was found by Heurico 1.16 in 0.69 seconds.