The generator matrix

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

generates a code of length 22 over Z4[X]/(X^2+2,2X) who´s minimum homogenous weight is 16.

Homogenous weight enumerator: w(x)=1x^0+123x^16+298x^18+500x^20+512x^21+1234x^22+512x^23+499x^24+302x^26+92x^28+22x^30+1x^40

The gray image is a code over GF(2) with n=88, k=12 and d=32.
This code was found by Heurico 1.16 in 0.253 seconds.