The generator matrix

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

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+54x^45+223x^46+230x^47+422x^48+410x^49+893x^50+556x^51+1073x^52+636x^53+1033x^54+518x^55+874x^56+380x^57+352x^58+202x^59+152x^60+46x^61+55x^62+28x^63+31x^64+10x^65+3x^66+2x^67+7x^68+1x^70

The gray image is a linear code over GF(2) with n=212, k=13 and d=90.
This code was found by Heurico 1.16 in 34.8 seconds.