The generator matrix

 1  0  1  1  1  0  1  1  X  1  1 X+2  X  X  0  2  X  2 X+2  1  1  1
 0  1  1  0 X+1  1  X X+3  1 X+2  3  1  2  X  1  1  1  X  1  0 X+3  0
 0  0  X X+2  0 X+2  X X+2  X  2  0  0  X  X  0  X  X  X  0  0  X  0
 0  0  0  2  0  0  0  0  0  0  2  2  0  2  0  0  2  0  2  2  2  2
 0  0  0  0  2  0  0  0  0  0  2  0  2  2  0  2  0  0  2  0  2  0
 0  0  0  0  0  2  0  0  0  2  2  0  2  0  2  2  2  0  0  2  2  0
 0  0  0  0  0  0  2  0  0  0  2  2  2  0  0  2  2  2  2  0  2  2
 0  0  0  0  0  0  0  2  0  2  0  2  2  0  0  2  0  2  0  2  2  0
 0  0  0  0  0  0  0  0  2  2  2  0  0  2  2  2  2  0  2  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+43x^14+62x^15+177x^16+276x^17+671x^18+1236x^19+1869x^20+2516x^21+2654x^22+2528x^23+1878x^24+1244x^25+702x^26+268x^27+162x^28+60x^29+23x^30+2x^31+8x^32+3x^34+1x^36

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 2.16 seconds.