The generator matrix

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

generates a code of length 44 over Z2[X]/(X^3) who´s minimum homogenous weight is 36.

Homogenous weight enumerator: w(x)=1x^0+44x^36+88x^37+214x^38+390x^39+486x^40+638x^41+839x^42+970x^43+997x^44+946x^45+788x^46+610x^47+455x^48+310x^49+180x^50+102x^51+58x^52+30x^53+26x^54+8x^55+6x^56+4x^57+1x^58+1x^60

The gray image is a linear code over GF(2) with n=176, k=13 and d=72.
This code was found by Heurico 1.16 in 2.51 seconds.