The generator matrix

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

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+8x^21+108x^22+8x^23+1x^24+1x^28+1x^36

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.