The generator matrix

 1  1  1  1  1  1  1  1  1  1  X  0  X  X  1  1  0  1  1  1  1  X
 0  X  0 X+2  0 X+2  0 X+2  2 X+2 X+2  X X+2 X+2  0  0  X X+2 X+2 X+2  0 X+2
 0  0  2  0  0  0  0  0  2  0  0  0  2  2  0  2  2  0  2  0  0  2
 0  0  0  2  0  0  0  0  0  0  2  2  2  2  0  0  0  0  0  2  2  2
 0  0  0  0  2  0  0  0  0  0  2  2  2  2  2  2  2  2  2  2  0  2
 0  0  0  0  0  2  0  0  0  2  0  0  2  2  2  0  0  2  0  2  0  2
 0  0  0  0  0  0  2  0  2  0  0  2  0  2  2  2  0  0  2  2  0  0
 0  0  0  0  0  0  0  2  0  2  2  0  0  2  2  2  0  0  2  0  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+83x^16+176x^18+485x^20+544x^22+514x^24+176x^26+58x^28+10x^32+1x^36

The gray image is a code over GF(2) with n=88, k=11 and d=32.
This code was found by Heurico 1.16 in 0.0687 seconds.