The generator matrix

 1  0  1  1  1 X+2  1  1 X+2  1  1  1  2  1  X  1 2X  1  1 3X+2  1  1
 0  1  1 2X+2 X+1  1  0 X+3  1  1  X 2X+1  1  0 X+2 3X  X X+2 3X  1 X+3 2X
 0  0  X 3X 2X 3X  2 X+2  2 2X+2 3X 3X+2 X+2 3X+2  X 2X  X  2  X 2X 3X+2 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+78x^19+300x^20+424x^21+591x^22+280x^23+219x^24+96x^25+32x^26+18x^27+8x^28+1x^30

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 0.031 seconds.