The generator matrix

 1  0  0  1  1  1 X+2  1  0  1  1  X  1  2  X  1  1  1  1 X+2  1  X
 0  1  0  0  1 X+3  1  X  1  3 X+2  1  1  X  1  X X+1  X  3 X+2  X  X
 0  0  1 X+1  1 X+2 X+1  X X+1 X+1 X+1  X  X  1  1  1 X+1 X+2  2  1  3 X+2
 0  0  0  2  0  0  2  0  2  0  0  2  2  2  0  2  2  2  2  0  2  0
 0  0  0  0  2  0  2  2  0  0  2  2  2  0  0  2  0  0  2  0  2  2
 0  0  0  0  0  2  2  2  0  2  0  0  2  2  0  0  2  0  0  2  2  0

generates a code of length 22 over Z4[X]/(X^2+2,2X) who´s minimum homogenous weight is 17.

Homogenous weight enumerator: w(x)=1x^0+88x^17+168x^18+450x^19+343x^20+748x^21+523x^22+750x^23+347x^24+432x^25+131x^26+78x^27+13x^28+12x^29+9x^30+2x^31+1x^34

The gray image is a code over GF(2) with n=88, k=12 and d=34.
This code was found by Heurico 1.16 in 0.158 seconds.