The generator matrix

 1  0  0  0  1  1  1  0  1  2  2  1  1  1  X  1  2  X  1  1  1  1
 0  1  0  0  0  1  3  1  X  X  1  1 X+2  3  X  0  1  1 X+3 X+1 X+2  0
 0  0  1  0  1  1  0 X+1 X+1  1 X+3  1  X  0  1  3 X+1  2 X+2  1  2  0
 0  0  0  1  1  0 X+1 X+1  X X+1  X  3  1  0 X+1  X  2 X+1  3 X+3  2  2
 0  0  0  0  2  0  2  0  0  0  2  2  0  2  2  2  2  0  2  0  0  0
 0  0  0  0  0  2  2  2  0  0  2  2  2  0  2  2  0  0  0  0  2  2

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+69x^16+340x^17+714x^18+1456x^19+1583x^20+2732x^21+2421x^22+2992x^23+1645x^24+1372x^25+633x^26+288x^27+93x^28+36x^29+7x^30+1x^32+1x^34

The gray image is a code over GF(2) with n=88, k=14 and d=32.
This code was found by Heurico 1.16 in 2.37 seconds.