The generator matrix

 1  1  1  1  1  1  1  1  X  0  1  1  1  X  1  2  1 2X+2  X  1  1
 0  X  0 X+2 2X+2 3X+2  2  X 3X+2  X 3X+2  X 3X+2 X+2 3X+2  X  2 2X+2 X+2 3X+2  0
 0  0  2  0 2X+2  0  0 2X 2X  2 2X+2  2 2X+2  2 2X+2  2  2  0 2X+2 2X+2 2X
 0  0  0  2  0  0 2X 2X+2 2X  2  2  0  2 2X 2X  2 2X+2 2X+2 2X  0 2X
 0  0  0  0 2X 2X 2X 2X  0  0  0  0 2X  0  0 2X  0 2X 2X  0  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+27x^16+114x^17+190x^18+452x^19+811x^20+940x^21+811x^22+416x^23+174x^24+114x^25+20x^26+12x^27+11x^28+3x^30

The gray image is a code over GF(2) with n=168, k=12 and d=64.
This code was found by Heurico 1.16 in 0.094 seconds.