The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+3x^44+24x^45+3x^46+1x^58

The gray image is a linear code over GF(2) with n=176, k=5 and d=88.
This code was found by Heurico 1.16 in 0.0253 seconds.