The generator matrix

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

generates a code of length 22 over Z4[X]/(X^2+2,2X) who´s minimum homogenous weight is 16.

Homogenous weight enumerator: w(x)=1x^0+85x^16+340x^17+778x^18+1178x^19+1945x^20+2288x^21+3007x^22+2406x^23+2124x^24+1164x^25+656x^26+264x^27+101x^28+32x^29+7x^30+6x^31+2x^35

The gray image is a code over GF(2) with n=88, k=14 and d=32.
This code was found by Heurico 1.13 in 0.969 seconds.