The generator matrix

 1  0  0  0  1  1  1  1  2  1  1  1  X  0 X+2  1 X+2  2  2  2  X  1
 0  1  0  0  0  1  2  3  1 X+2  3 X+3  1  1  0  2  1  X  1  X  1  2
 0  0  1  0  0  1  3  2  3  1 X+1  X  X X+1  1 X+3 X+2  1  1  1 X+1  X
 0  0  0  1 X+1  2  1  3  3 X+2 X+3  2 X+3  2 X+3 X+2  3 X+3  0  1 X+3 X+1
 0  0  0  0  2  0  0  0  0  2  2  2  2  2  2  0  0  0  2  2  0  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+194x^17+361x^18+762x^19+821x^20+1286x^21+1254x^22+1460x^23+781x^24+734x^25+333x^26+162x^27+28x^28+10x^29+4x^30+1x^36

The gray image is a code over GF(2) with n=88, k=13 and d=34.
This code was found by Heurico 1.13 in 0.273 seconds.