The generator matrix

 1  0  0  0  1  1  1 X+2 X^2+X  1  1 X+2  1 X+2  1  1  1  1  0 X^2+2  1  1
 0  1  0  0 X^2  3 X^2+1  1  1 X^2+X X+3 X^2+X X^2+X+2  1 X^2+X+3 X^2+3  X X+1  1 X^2+2  0  0
 0  0  1  0 X^2+1  1 X^2 X^2+X+1  1 X+1 X^2+X+3  1  X  2  3 X^2+X X+3 X^2+X X^2+X+1  1 X+1  2
 0  0  0  1  1 X^2 X^2+X+1 X^2+X+1 X+2  0 X+3 X+1  3 X^2+1 X^2+X+3 X^2+X+2 X+2  2 X^2+3  1 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+128x^17+1086x^18+2878x^19+7533x^20+12848x^21+16496x^22+13006x^23+7671x^24+2664x^25+974x^26+210x^27+27x^28+8x^29+4x^30+2x^31

The gray image is a code over GF(2) with n=176, k=16 and d=68.
This code was found by Heurico 1.16 in 9.37 seconds.