The generator matrix

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

generates a code of length 52 over Z2[X]/(X^3) who´s minimum homogenous weight is 44.

Homogenous weight enumerator: w(x)=1x^0+159x^44+48x^45+364x^46+260x^47+659x^48+552x^49+858x^50+688x^51+1082x^52+680x^53+894x^54+536x^55+637x^56+248x^57+266x^58+48x^59+109x^60+8x^61+46x^62+4x^63+30x^64+4x^66+10x^68+1x^72

The gray image is a linear code over GF(2) with n=208, k=13 and d=88.
This code was found by Heurico 1.16 in 3.17 seconds.