The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+154x^19+588x^20+876x^21+1138x^22+588x^23+435x^24+220x^25+70x^26+18x^27+8x^28

The gray image is a code over GF(2) with n=176, k=12 and d=76.
This code was found by Heurico 1.16 in 0.047 seconds.