The generator matrix

 1  0  1  1  1  0  1  1  2  1  1 X+2  1  1  1  1  1  2  2  1  1  1
 0  1  1  0 X+1  1  0 X+1  1  X X+3  1  3  1 X+1  1 X+3  1  1  1 X+3  0
 0  0  X  0  X  0  X  0  X  X  0  X  X  0  2 X+2  0  2  X  X  0  0
 0  0  0  X  X X+2  X  0  0  0  X  X  X X+2  0  2 X+2  X  2  2  X  0
 0  0  0  0  2  0  0  0  0  2  0  2  2  2  0  0  2  2  2  2  2  0
 0  0  0  0  0  2  0  0  2  2  2  2  2  0  2  0  0  0  2  0  0  0
 0  0  0  0  0  0  2  0  0  0  2  2  0  2  2  0  0  2  2  2  0  0
 0  0  0  0  0  0  0  2  2  2  0  0  2  2  2  2  2  2  2  2  0  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+37x^14+94x^15+152x^16+328x^17+605x^18+844x^19+2016x^20+2804x^21+2554x^22+2840x^23+2052x^24+900x^25+610x^26+308x^27+112x^28+60x^29+33x^30+10x^31+19x^32+4x^33+1x^34

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 2.22 seconds.