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  1  1  1  1  1  1  1  1  X  1  X  0  1  1  1 X^2  X  1  0  1  X  X  1  1  1  X  0  X  1
 0  X  0  0  0  0  0  0  0  X X^2+X  X X^2 X^2+X X^2  X  X  X  0 X^2+X  X X^2+X X^2  X X^2  X  0  X X^2  0 X^2+X X^2+X X^2+X X^2  X  0 X^2+X  X X^2+X  X X^2+X  X  X  X  X  X X^2  0 X^2+X  X  0  0 X^2+X
 0  0  X  0  0  0  X X^2+X  X  X  X  0  0 X^2+X X^2 X^2 X^2 X^2  X X^2+X  X  0  X X^2+X X^2 X^2+X  0  0 X^2+X  X  X X^2  X  0 X^2+X X^2 X^2+X X^2+X X^2+X  0 X^2 X^2+X  X  0  X  X X^2+X  0 X^2  X  X  X  0
 0  0  0  X  0  X  X  X X^2  0  0 X^2 X^2 X^2+X  0  X X^2 X^2+X  X X^2+X  X  X X^2 X^2  X X^2+X  X X^2 X^2 X^2+X X^2  X X^2 X^2+X X^2+X  X X^2 X^2 X^2+X  0  X  0  X X^2 X^2 X^2+X X^2 X^2+X X^2+X  X  X X^2+X X^2
 0  0  0  0  X  X X^2 X^2+X X^2+X  0  X  X  0  0  X  X X^2+X  0 X^2  X  0  X X^2 X^2 X^2+X X^2+X X^2  0  X X^2+X  X X^2  X  X X^2+X X^2  X  X X^2 X^2+X  X X^2 X^2 X^2  0  0 X^2 X^2  X  X X^2  0  0
 0  0  0  0  0 X^2 X^2 X^2 X^2 X^2  0  0 X^2  0 X^2 X^2 X^2  0  0  0 X^2  0 X^2  0  0 X^2 X^2 X^2  0  0 X^2 X^2  0 X^2  0  0  0 X^2  0 X^2  0  0 X^2 X^2 X^2 X^2  0  0 X^2 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+68x^45+112x^46+146x^47+186x^48+264x^49+289x^50+334x^51+484x^52+432x^53+431x^54+402x^55+255x^56+188x^57+149x^58+110x^59+85x^60+68x^61+37x^62+28x^63+10x^64+4x^65+6x^66+4x^67+2x^68+1x^84

The gray image is a linear code over GF(2) with n=212, k=12 and d=90.
This code was found by Heurico 1.16 in 1.03 seconds.