The generator matrix

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

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+132x^19+694x^20+758x^21+1158x^22+536x^23+528x^24+206x^25+73x^26+9x^28+1x^30

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.