The generator matrix

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

generates a code of length 44 over Z2[X]/(X^3) who´s minimum homogenous weight is 42.

Homogenous weight enumerator: w(x)=1x^0+26x^42+16x^43+44x^44+16x^45+16x^46+1x^48+4x^50+2x^52+2x^54

The gray image is a linear code over GF(2) with n=176, k=7 and d=84.
This code was found by Heurico 1.16 in 0.0264 seconds.