The generator matrix

 1  1  1  1  1  1  1  1  1  1  X  X  1  1  1 2X+2  X  1  1  1 2X+2  X
 0  X  0  X  0 2X 3X+2 2X+2 3X+2 2X+2 2X+2 3X+2 3X  2 3X  X 3X  2  2 2X  X 2X+2
 0  0  X  X  2 X+2 3X+2  2 2X  0  X  0 3X+2  X  2  X X+2 3X+2 2X+2  0  X  X
 0  0  0 2X  0  0  0 2X 2X 2X  0  0 2X  0 2X  0  0 2X  0 2X 2X 2X
 0  0  0  0 2X 2X  0  0 2X 2X  0 2X  0  0 2X 2X  0 2X  0 2X  0  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+105x^18+264x^19+445x^20+652x^21+1220x^22+616x^23+428x^24+240x^25+81x^26+16x^27+21x^28+4x^29+2x^30+1x^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 0.094 seconds.