The generator matrix

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

generates a code of length 22 over Z2[X]/(X^4) who´s minimum homogenous weight is 21.

Homogenous weight enumerator: w(x)=1x^0+8x^21+108x^22+8x^23+1x^24+1x^28+1x^36

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 6.87e-008 seconds.