The generator matrix

 1  1  1  1  1  1  1  1  1  1  X  1  1  1  X  0  1  X X^2+2  1  2  1
 0  X  0  X  2  0 X^2+X X^2+X X^2 X^2+2 X^2+X X^2+X+2 X+2  0 X^2+X  0  2 X^2  X X+2 X^2 X+2
 0  0  X  X X^2 X^2+X X^2+X  0 X^2+2  0  2 X^2 X+2  X X^2+X+2  X X^2+X+2 X^2+X+2 X^2+X X^2+X X^2+2 X^2+2
 0  0  0  2  2  2  0  2  0  2  0  0  0  2  2  0  0  2  0  2  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+218x^19+158x^20+584x^21+192x^22+534x^23+158x^24+152x^25+46x^27+2x^28+2x^31+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 14.5 seconds.