The generator matrix

 1  1  1  1  1  1  1  1  1  1  1  1  1  X  X  X  1  X  1  1  X  1
 0  X  0  0  0  X X+2  X  2  2  0  0  X  0  X  2  X  X  X X+2  0  0
 0  0  X  0  X  X  X  0  2  0  X X+2 X+2  0  2  2  X X+2  0  0  X  0
 0  0  0  X  X  0  X X+2  0  X  X  2  2 X+2  X X+2  2  2 X+2 X+2  X  0
 0  0  0  0  2  0  0  0  2  2  2  0  2  0  2  0  2  2  2  0  2  0
 0  0  0  0  0  2  0  2  0  0  2  2  0  2  0  0  2  2  2  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+51x^16+56x^17+93x^18+100x^19+313x^20+92x^21+620x^22+120x^23+311x^24+96x^25+106x^26+36x^27+27x^28+12x^29+12x^30+1x^32+1x^34

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 0.0663 seconds.