The generator matrix

 1  0  0  1  1  1  X  2  1  1  1  2 X+2  1  1 X+2  X  1  1 X+2  0  1
 0  1  0  1  0 X+3  1  X X+2 X+2 X+3  1  1 X+1  3  X  1  X  X  1 X+2 X+3
 0  0  1  1  1  0  1  1  X  1 X+1  1  2  0 X+1  1  3  X  2 X+2  1  2
 0  0  0  X  0 X+2  2  X  2  X  0 X+2  2  0  0 X+2  2  0  X  0  X  2
 0  0  0  0  X  0  2 X+2 X+2  0  X X+2  2  2  0  0  X  2  X  X  2  0
 0  0  0  0  0  2  2  2  2  2  2  0  0  0  2  0  2  2  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+169x^16+256x^17+749x^18+968x^19+2236x^20+2352x^21+2924x^22+2352x^23+2216x^24+1024x^25+755x^26+200x^27+144x^28+16x^29+19x^30+2x^32+1x^38

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 2.82 seconds.