The generator matrix

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

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+108x^19+761x^20+658x^21+1280x^22+434x^23+592x^24+168x^25+79x^26+6x^27+6x^28+2x^29+1x^30

The gray image is a code over GF(2) with n=176, k=12 and d=76.
This code was found by Heurico 1.16 in 0.047 seconds.