The generator matrix

 1  0  0  1  1  1  0  1  1  X X+2  1  0  1 X+2  X  1  1  0  1  1  X
 0  1  0  1  X X+3  1  0 X+3  1  X  2  1 X+1  1  1 X+1  1  2 X+1 X+2  1
 0  0  1  1  1  0 X+3  X  X  1  1  1  X X+1  X  X  X  X  1 X+3  X  0
 0  0  0  X  0 X+2 X+2  X  2  2 X+2  0 X+2  0 X+2  2  X  0 X+2 X+2  X X+2
 0  0  0  0  2  0  0  2  2  2  2  2  2  2  0  2  2  0  2  2  0  0
 0  0  0  0  0  2  0  0  0  2  0  2  0  2  0  2  0  0  2  2  2  0
 0  0  0  0  0  0  2  2  0  2  2  2  2  0  0  0  0  2  0  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+185x^16+200x^17+776x^18+1064x^19+2150x^20+2320x^21+2992x^22+2320x^23+2150x^24+1064x^25+776x^26+200x^27+185x^28+1x^44

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 2.34 seconds.