The generator matrix

 1  0  1  1  1  0  1  1  2  1  1 X+2  1  1  0  1  1  0  X  X  1  1
 0  1  1  0 X+1  1 X+3  0  1  2  3  1  X X+3  1 X+3  2  1  X  2 X+3 X+1
 0  0  X  0  0  0  0  X  X X+2 X+2  2 X+2 X+2  2  0  2  0  X  0 X+2 X+2
 0  0  0  X  0 X+2 X+2  X  2  2  X  2  2  2  2 X+2 X+2  2  2 X+2  2  2
 0  0  0  0  2  0  0  2  2  0  0  0  2  2  2  0  0  2  2  2  0  2
 0  0  0  0  0  2  0  0  0  0  0  2  2  2  0  2  2  2  2  2  0  2
 0  0  0  0  0  0  2  0  0  2  0  0  0  2  2  2  0  2  2  0  0  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+169x^16+72x^17+400x^18+552x^19+854x^20+1424x^21+1248x^22+1424x^23+854x^24+552x^25+400x^26+72x^27+169x^28+1x^44

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 0.84 seconds.