The generator matrix

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

generates a code of length 22 over Z4[X]/(X^2+2) who´s minimum homogenous weight is 17.

Homogenous weight enumerator: w(x)=1x^0+50x^17+540x^18+1476x^19+3635x^20+6586x^21+8177x^22+6698x^23+3617x^24+1342x^25+522x^26+96x^27+17x^28+6x^29+1x^30+2x^31+2x^32

The gray image is a code over GF(2) with n=176, k=15 and d=68.
This code was found by Heurico 1.16 in 2.48 seconds.