The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+31x^18+204x^19+385x^20+1100x^21+707x^22+1064x^23+377x^24+168x^25+29x^26+12x^27+3x^28+12x^29+1x^30+2x^32

The gray image is a code over GF(2) with n=176, k=12 and d=72.
This code was found by Heurico 1.16 in 0.062 seconds.