The generator matrix

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

generates a code of length 22 over Z4[X]/(X^2+2) who´s minimum homogenous weight is 20.

Homogenous weight enumerator: w(x)=1x^0+30x^20+192x^22+30x^24+2x^28+1x^32

The gray image is a code over GF(2) with n=176, k=8 and d=80.
This code was found by Heurico 1.16 in 6.87e-008 seconds.