The generator matrix

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

generates a code of length 44 over Z2[X]/(X^3) who´s minimum homogenous weight is 35.

Homogenous weight enumerator: w(x)=1x^0+50x^35+152x^36+166x^37+203x^38+290x^39+554x^40+570x^41+701x^42+962x^43+939x^44+974x^45+669x^46+602x^47+532x^48+286x^49+172x^50+132x^51+108x^52+52x^53+39x^54+12x^55+16x^56+7x^58+1x^60+1x^62+1x^64

The gray image is a linear code over GF(2) with n=176, k=13 and d=70.
This code was found by Heurico 1.16 in 3.85 seconds.