The generator matrix

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

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+122x^20+64x^21+160x^22+64x^23+86x^24+14x^28+1x^32

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 18.5 seconds.