The generator matrix

 1  0  1  1  1  X  1  1 X^2+X+2  1  1  1  0  1  1  X  1  1  1  1  X  1
 0  1  1 X^2 X+1  1  0 X^2+X+3  1  1  X  3  1  0 X^2+X X^2+X X+3 X^2+X+3  X  1 X^2 X^2
 0  0  X X+2  2 X+2 X^2+2 X^2+X+2 X^2+2 X^2 X+2 X^2+X X^2+X+2 X^2+X  0 X^2+X X^2  X X^2+X+2  0  X X^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+76x^19+296x^20+444x^21+588x^22+244x^23+238x^24+116x^25+20x^26+16x^27+8x^28+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.