The generator matrix

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

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+83x^16+222x^17+308x^18+736x^19+778x^20+1294x^21+1188x^22+1456x^23+876x^24+698x^25+284x^26+176x^27+54x^28+26x^29+12x^30

The gray image is a code over GF(2) with n=88, k=13 and d=32.
This code was found by Heurico 1.16 in 0.706 seconds.