The generator matrix

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

generates a code of length 22 over Z4[X]/(X^2+2X+2) who´s minimum homogenous weight is 19.

Homogenous weight enumerator: w(x)=1x^0+156x^19+245x^20+434x^21+444x^22+436x^23+168x^24+88x^25+28x^26+32x^27+9x^28+6x^29+1x^32

The gray image is a code over GF(2) with n=176, k=11 and d=76.
This code was found by Heurico 1.16 in 4.7 seconds.