The generator matrix

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

generates a code of length 53 over Z2[X]/(X^3) who´s minimum homogenous weight is 44.

Homogenous weight enumerator: w(x)=1x^0+19x^44+72x^45+138x^46+292x^47+380x^48+486x^49+673x^50+840x^51+863x^52+834x^53+900x^54+664x^55+633x^56+572x^57+280x^58+232x^59+123x^60+68x^61+48x^62+20x^63+23x^64+14x^65+7x^66+3x^68+2x^69+2x^70+3x^72

The gray image is a linear code over GF(2) with n=212, k=13 and d=88.
This code was found by Heurico 1.16 in 3.11 seconds.