The generator matrix

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

generates a code of length 21 over Z4[X]/(X^2+2X+2) who´s minimum homogenous weight is 16.

Homogenous weight enumerator: w(x)=1x^0+98x^16+618x^17+1611x^18+3318x^19+6458x^20+8480x^21+6590x^22+3406x^23+1469x^24+546x^25+151x^26+10x^27+4x^28+4x^29+2x^31+2x^32

The gray image is a code over GF(2) with n=168, k=15 and d=64.
This code was found by Heurico 1.16 in 2.47 seconds.