The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+106x^20+64x^22+70x^24+14x^28+1x^32

The gray image is a code over GF(2) with n=88, k=8 and d=40.
This code was found by Heurico 1.16 in 1.35 seconds.