The generator matrix

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

generates a code of length 23 over Z4[X]/(X^2+2,2X) who´s minimum homogenous weight is 20.

Homogenous weight enumerator: w(x)=1x^0+121x^20+96x^22+250x^24+43x^28+1x^40

The gray image is a code over GF(2) with n=92, k=9 and d=40.
This code was found by Heurico 1.16 in 0.648 seconds.