The generator matrix

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

generates a code of length 22 over Z4[X]/(X^2+2,2X) who´s minimum homogenous weight is 14.

Homogenous weight enumerator: w(x)=1x^0+71x^14+124x^15+259x^16+332x^17+443x^18+574x^19+787x^20+3064x^21+5059x^22+3034x^23+797x^24+652x^25+480x^26+290x^27+201x^28+112x^29+90x^30+10x^31+3x^32+1x^42

The gray image is a code over GF(2) with n=88, k=14 and d=28.
This code was found by Heurico 1.16 in 3.43 seconds.