The generator matrix

 1  1  1  1  1  1  1  1  1  1  X  1  1  2  X  2  X  X  X  2  X  1
 0  X  0  0  0  0  0  0  2 X+2 X+2  X X+2  2  X  X X+2 X+2  X  0  2  0
 0  0  X  0  0  0  X X+2 X+2  X  X  0 X+2  2  X  0  0  X  2  X  2  0
 0  0  0  X  0  X  X X+2  0  0 X+2  X  X  X X+2  X  0  2  0  0  2  0
 0  0  0  0  X  X  0 X+2  X  X  2  0  X X+2 X+2  0  0  X  X X+2  X  0
 0  0  0  0  0  2  0  0  0  0  0  2  2  2  2  0  2  0  2  0  2  0
 0  0  0  0  0  0  2  0  0  2  0  0  2  2  2  2  0  0  0  2  0  0
 0  0  0  0  0  0  0  2  2  2  0  2  0  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 14.

Homogenous weight enumerator: w(x)=1x^0+72x^14+138x^15+269x^16+508x^17+462x^18+1760x^19+720x^20+3728x^21+980x^22+3724x^23+822x^24+1808x^25+464x^26+512x^27+232x^28+96x^29+68x^30+10x^31+4x^32+4x^33+2x^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 3.22 seconds.