The generator matrix

 1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  X  X
 0  X  0 X^3+X^2+X X^2 X^2+X X^3+X^2  X X^2+X  0 X^3 X^2+X X^3+X^2 X^3+X^2 X^3+X  X X^3 X^3 X^3 X^2 X^2+X X^3+X^2+X
 0  0 X^3+X^2 X^2 X^2 X^3 X^3 X^2  0 X^3 X^2 X^3+X^2 X^3+X^2  0 X^3+X^2 X^3 X^3  0 X^3+X^2 X^3  0 X^2

generates a code of length 22 over Z2[X]/(X^4) who´s minimum homogenous weight is 20.

Homogenous weight enumerator: w(x)=1x^0+71x^20+64x^21+240x^22+64x^23+70x^24+1x^28+1x^40

The gray image is a linear code over GF(2) with n=176, k=9 and d=80.
This code was found by Heurico 1.16 in 0.015 seconds.