The generator matrix

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

generates a code of length 22 over Z4[X]/(X^3+2,2X) who´s minimum homogenous weight is 17.

Homogenous weight enumerator: w(x)=1x^0+44x^17+606x^18+1422x^19+3587x^20+6334x^21+8760x^22+6452x^23+3611x^24+1232x^25+566x^26+126x^27+17x^28+6x^29+4x^30

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 2.41 seconds.