The generator matrix

 1  0  0  1  1  1 X^2+X  1  X  0  1  1 X^2  1  1  1 X^2+X X^2+X  1  1  1 X^2+X X^2+X X^2+X  1  1  0  1  0  1  1  1 X^2+X  1  1 X^2  0  1 X^2+X X^2  X  X  1 X^2  1  1  X  1  1  1  X  1  1
 0  1  0  0  1  1  1 X^2  1  0 X^2+1 X^2+X  1 X^2+X+1 X+1 X^2+X+1  1  1  X  X X+1  X X^2  1  X X+1  X  X  1 X^2+1 X^2+X X^2+1  0 X+1 X^2  0  1 X^2  1  1  1  1  0  1  X X^2+X+1  0 X^2+1 X^2  0 X^2 X^2+X  1
 0  0  1  1  1  0  1 X^2 X^2+1  1  0 X^2+X+1  0 X+1  1  X X^2+1  X  0 X+1  1  1  1 X^2+1 X^2+1 X^2  1 X^2 X^2+X  1  X  0  1  0  1  1  X  0 X^2 X^2+1 X^2+X X^2+1  1 X^2  X X^2+X+1  1 X+1 X+1  X  1 X^2+X+1  X
 0  0  0  X  0  0  0  0  0  0 X^2  X X^2+X X^2 X^2 X^2+X X^2+X  X X^2+X  0  X X^2+X X^2+X  X  0  X X^2 X^2 X^2+X X^2+X X^2+X X^2+X  X  0  0 X^2+X X^2 X^2  X X^2+X X^2  X  0 X^2 X^2+X X^2  0 X^2+X  X X^2+X X^2+X  X  X
 0  0  0  0  X  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0 X^2 X^2 X^2 X^2 X^2 X^2  X X^2+X  X X^2+X  X X^2+X X^2+X X^2+X X^2+X  X X^2+X X^2+X  X X^2  X X^2 X^2+X X^2+X X^2+X X^2 X^2 X^2+X  X X^2  X X^2+X
 0  0  0  0  0  X X^2+X X^2+X X^2  X X^2 X^2+X  0  X X^2 X^2+X X^2+X X^2+X  X  0 X^2 X^2  X X^2 X^2+X  0  0  0 X^2+X X^2+X X^2  X X^2+X X^2 X^2  0 X^2+X X^2+X  0  X  0  X  0  X  X X^2+X X^2 X^2 X^2 X^2 X^2  X 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+235x^44+216x^45+820x^46+796x^47+1748x^48+1740x^49+2788x^50+2700x^51+3564x^52+3400x^53+3756x^54+2696x^55+2938x^56+1852x^57+1568x^58+748x^59+645x^60+152x^61+252x^62+36x^63+81x^64+28x^66+4x^68+4x^70

The gray image is a linear code over GF(2) with n=212, k=15 and d=88.
This code was found by Heurico 1.16 in 36.1 seconds.