The generator matrix

 1  0  0  1  1  1 3X  1  1  2  1 3X+2 3X+2  1  1  X  1 3X  1  1 X+2  1
 0  1  0 2X+2  1 3X+1  1 3X  3  1  0 2X  1 3X+1  1 3X X+2 3X+2  2 2X+2  1  0
 0  0  1 3X+3  1 2X+2 2X+3 2X+3  X X+1 3X+2  1 3X+2 2X+1 3X+3  1 3X+1  1 3X+1 2X+3 X+2  0
 0  0  0 2X 2X 2X  0  0  0 2X 2X 2X 2X  0  0 2X  0  0  0 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+35x^18+480x^19+1052x^20+1356x^21+2420x^22+1364x^23+955x^24+408x^25+69x^26+36x^27+8x^28+4x^29+4x^30

The gray image is a code over GF(2) with n=176, k=13 and d=72.
This code was found by Heurico 1.16 in 0.171 seconds.