The generator matrix

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

generates a code of length 22 over Z4[X]/(X^2+2,2X) who´s minimum homogenous weight is 15.

Homogenous weight enumerator: w(x)=1x^0+70x^15+172x^16+288x^17+694x^18+980x^19+1826x^20+2726x^21+2778x^22+2784x^23+1895x^24+1030x^25+666x^26+252x^27+134x^28+50x^29+22x^30+10x^31+3x^32+2x^33+1x^40

The gray image is a code over GF(2) with n=88, k=14 and d=30.
This code was found by Heurico 1.16 in 5.94 seconds.