The generator matrix

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

generates a code of length 21 over Z4[X]/(X^2+2) who´s minimum homogenous weight is 19.

Homogenous weight enumerator: w(x)=1x^0+176x^19+209x^20+320x^21+152x^22+112x^23+20x^24+32x^25+1x^28+1x^32

The gray image is a code over GF(2) with n=168, k=10 and d=76.
This code was found by Heurico 1.16 in 0.015 seconds.