The generator matrix

 1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  X  1  0  X  X  X  0
 0  X  0 X+2  0 X+2  0  X  0 X+2  2  X  2  0  X X+2 X+2  X  2  2 X+2  X
 0  0  2  0  0  0  2  0  0  2  2  2  2  2  0  0  2  0  2  0  0  2
 0  0  0  2  0  0  0  2  2  2  2  2  0  2  2  0  0  0  0  2  2  0
 0  0  0  0  2  2  2  2  2  0  2  0  0  2  0  0  2  0  2  0  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+103x^20+64x^22+78x^24+8x^28+1x^32+1x^36

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 2.18 seconds.