The generator matrix

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

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+330x^20+384x^22+294x^24+14x^28+1x^32

The gray image is a linear code over GF(2) with n=176, k=10 and d=80.
This code was found by Heurico 1.16 in 0.031 seconds.