The generator matrix

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

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+107x^18+80x^19+476x^20+1008x^21+766x^22+1008x^23+468x^24+80x^25+84x^26+12x^28+2x^30+3x^32+1x^34

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 35.9 seconds.