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  0  0  0  0  0 X+2 X+2  X  X  X  X  0  X  2  X  X  2  X  X
 0  0  X  0  0  0  X X+2  X  X  2  X  X  0 X+2  2  2  X  X  0 X+2  X
 0  0  0  X  0  X  X  X  2  X X+2  X  2  2  2 X+2  X  0  X X+2  2  X
 0  0  0  0  X  X  0  X  X  0  X  X  0 X+2 X+2  0  X  2  X  X  2  X
 0  0  0  0  0  2  0  0  0  0  0  0  2  0  2  2  0  2  2  0  2  2
 0  0  0  0  0  0  2  0  0  0  0  0  0  2  2  2  2  2  0  2  2  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+514x^16+256x^18+2496x^20+1536x^22+2712x^24+256x^26+384x^28+37x^32

The gray image is a code over GF(2) with n=88, k=13 and d=32.
This code was found by Heurico 1.16 in 14.2 seconds.