The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+145x^16+894x^17+3875x^18+11218x^19+29432x^20+52180x^21+66121x^22+52852x^23+29704x^24+11030x^25+3621x^26+794x^27+204x^28+56x^29+15x^30+2x^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 130 seconds.