The generator matrix

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

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+14x^21+103x^22+7x^24+2x^29+1x^30

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 0.016 seconds.