The generator matrix

 1  1  1  1  1  1  1  1  X  X  X  X  1  X  X  X  1  1  1  1  1  1
 0 2X  0  0  0 2X 2X 2X  0  0 2X 2X  0  0 2X 2X  0  0 2X  0 2X 2X
 0  0 2X  0 2X 2X 2X  0  0 2X 2X  0  0 2X 2X  0  0 2X 2X 2X 2X  0
 0  0  0 2X 2X  0 2X 2X 2X 2X  0  0  0  0 2X 2X 2X 2X  0  0 2X 2X

generates a code of length 22 over Z4[X]/(X^2+2) 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 code over GF(2) with n=176, k=7 and d=84.
This code was found by Heurico 1.16 in 0.016 seconds.