The generator matrix

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

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+108x^35+427x^36+1098x^37+1708x^38+2614x^39+3824x^40+5166x^41+6423x^42+7424x^43+8013x^44+7274x^45+6409x^46+5314x^47+3963x^48+2722x^49+1529x^50+842x^51+369x^52+180x^53+91x^54+16x^55+8x^56+8x^57+2x^59+3x^60

The gray image is a linear code over GF(2) with n=176, k=16 and d=70.
This code was found by Heurico 1.13 in 30.9 seconds.