The generator matrix

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

generates a code of length 22 over Z4[X]/(X^3+2,2X) who´s minimum homogenous weight is 16.

Homogenous weight enumerator: w(x)=1x^0+124x^16+908x^17+3768x^18+11770x^19+28222x^20+53946x^21+64541x^22+53750x^23+28843x^24+11880x^25+3298x^26+830x^27+212x^28+34x^29+9x^30+2x^31+6x^32

The gray image is a code over GF(2) with n=176, k=18 and d=64.
This code was found by Heurico 1.16 in 126 seconds.