The generator matrix

 1  0  0  0  1  1  1 X^2  1  1  X  X X^2+X  1  1  1 X^2+X X^2+X X^2+X X^2+X  1 X^2+X X^2+X  1 X^2+X  1  1  1  1  1 X^2+X  X X^2+X  1 X^2+X  1 X^2+X  0  X  1  1  1  1  1  X  1  X  1  1  1  1  1
 0  1  0  0  0  1 X^2+1  1 X^2+1 X^2+X  1  1  X X^2+1 X^2 X^2+1 X^2+X X^2  1  1 X^2  0  1 X^2+X+1  1  X X+1 X+1 X^2+1 X^2  0  1  1 X^2+X  0 X^2+X  1  1 X^2+X  X X+1 X^2+1 X^2+X+1  X X^2 X^2 X^2+X  1  X  1 X^2 X^2
 0  0  1  0  1  1 X^2  1  0 X^2 X^2+X X+1  1 X+1 X^2+X+1  0  X  1  0  X X^2+1  1 X^2+X+1  0 X^2+X+1 X^2+1 X+1  0 X^2+X+1  X  1  0  X X^2 X^2+X X^2+X X^2+1  0  1 X^2+1 X^2+X+1 X^2 X^2+1  X  1 X^2+X+1  X  X X^2+X X^2+X+1  1  0
 0  0  0  1  1 X^2  1 X^2+1  0 X^2+1  1  0 X^2+1 X^2+1  X X^2+X+1  1 X^2+X+1  X  1 X^2+1 X^2+X X^2 X^2 X^2+1 X^2+X X^2  0 X+1  0  X X+1 X^2+X X+1  1  X X+1 X^2+X X+1 X^2+X+1  X  0  1  X X^2+1 X^2  1 X+1  1 X^2+X+1 X+1 X^2
 0  0  0  0  X  0  0  X X^2  X  X  0  X X^2+X X^2  X X^2+X  X X^2+X  0 X^2 X^2+X  X X^2 X^2 X^2+X X^2+X  X  0  X  0  0  X  X X^2 X^2 X^2 X^2 X^2+X X^2  0  X  X  0 X^2  0  0  X X^2 X^2 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+103x^44+368x^45+539x^46+818x^47+987x^48+1446x^49+1552x^50+1664x^51+1443x^52+1922x^53+1443x^54+1370x^55+970x^56+714x^57+452x^58+308x^59+132x^60+70x^61+44x^62+16x^63+8x^64+8x^65+2x^66+4x^68

The gray image is a linear code over GF(2) with n=208, k=14 and d=88.
This code was found by Heurico 1.13 in 2.84 seconds.