The generator matrix

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

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+280x^44+696x^45+1194x^46+1648x^47+2105x^48+2500x^49+2960x^50+3380x^51+3305x^52+3316x^53+3088x^54+2656x^55+2043x^56+1468x^57+1028x^58+580x^59+287x^60+116x^61+78x^62+24x^63+7x^64+4x^66+4x^68

The gray image is a linear code over GF(2) with n=208, k=15 and d=88.
This code was found by Heurico 1.16 in 32.4 seconds.