The generator matrix

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

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+402x^17+1936x^18+6298x^19+14079x^20+26268x^21+32348x^22+27358x^23+14419x^24+5700x^25+1648x^26+518x^27+77x^28+12x^29+4x^30+2x^31+2x^33

The gray image is a code over GF(2) with n=176, k=17 and d=68.
This code was found by Heurico 1.16 in 36.7 seconds.