The generator matrix

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

generates a code of length 44 over Z2[X]/(X^3) who´s minimum homogenous weight is 38.

Homogenous weight enumerator: w(x)=1x^0+254x^38+400x^39+708x^40+732x^41+788x^42+868x^43+901x^44+780x^45+817x^46+648x^47+575x^48+292x^49+240x^50+100x^51+51x^52+20x^53+11x^54+2x^56+2x^58+2x^60

The gray image is a linear code over GF(2) with n=176, k=13 and d=76.
This code was found by Heurico 1.11 in 0.719 seconds.