The generator matrix

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

generates a code of length 22 over Z4[X]/(X^2+2,2X) who´s minimum homogenous weight is 16.

Homogenous weight enumerator: w(x)=1x^0+49x^16+104x^17+194x^18+328x^19+438x^20+600x^21+666x^22+592x^23+492x^24+312x^25+150x^26+104x^27+42x^28+8x^29+14x^30+2x^32

The gray image is a code over GF(2) with n=88, k=12 and d=32.
This code was found by Heurico 1.16 in 0.177 seconds.