The generator matrix

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

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+87x^20+80x^22+85x^24+1x^28+2x^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 0.00485 seconds.