The generator matrix

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

generates a code of length 22 over Z4[X]/(X^2+2,2X) who´s minimum homogenous weight is 18.

Homogenous weight enumerator: w(x)=1x^0+254x^18+400x^19+530x^20+608x^21+608x^22+520x^23+557x^24+344x^25+186x^26+40x^27+40x^28+8x^29

The gray image is a code over GF(2) with n=88, k=12 and d=36.
This code was found by Heurico 1.16 in 1.18 seconds.