The generator matrix

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

generates a code of length 22 over Z4[X]/(X^3+2,2X) who´s minimum homogenous weight is 18.

Homogenous weight enumerator: w(x)=1x^0+214x^18+896x^19+1829x^20+3120x^21+4140x^22+3408x^23+1791x^24+720x^25+182x^26+48x^27+27x^28+8x^30

The gray image is a code over GF(2) with n=176, k=14 and d=72.
This code was found by Heurico 1.16 in 0.687 seconds.