The generator matrix

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

generates a code of length 22 over Z4[X]/(X^3+2,2X) who´s minimum homogenous weight is 19.

Homogenous weight enumerator: w(x)=1x^0+92x^19+246x^20+560x^21+272x^22+540x^23+246x^24+76x^25+8x^27+2x^28+4x^29+1x^32

The gray image is a code over GF(2) with n=176, k=11 and d=76.
This code was found by Heurico 1.16 in 0.016 seconds.