The generator matrix

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

generates a code of length 53 over Z2[X]/(X^3) who´s minimum homogenous weight is 45.

Homogenous weight enumerator: w(x)=1x^0+130x^45+309x^46+694x^47+923x^48+1064x^49+1284x^50+1454x^51+1649x^52+1496x^53+1545x^54+1588x^55+1305x^56+986x^57+822x^58+560x^59+239x^60+170x^61+100x^62+38x^63+8x^64+10x^65+4x^66+2x^67+2x^68+1x^72

The gray image is a linear code over GF(2) with n=212, k=14 and d=90.
This code was found by Heurico 1.13 in 2.94 seconds.