The generator matrix

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

generates a code of length 23 over Z4[X]/(X^2+2) who´s minimum homogenous weight is 22.

Homogenous weight enumerator: w(x)=1x^0+7x^22+110x^23+7x^24+1x^30+2x^31

The gray image is a code over GF(2) with n=184, k=7 and d=88.
This code was found by Heurico 1.16 in 0.015 seconds.