The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+99x^16+992x^17+2666x^18+7572x^19+12878x^20+16986x^21+13081x^22+7720x^23+2448x^24+884x^25+176x^26+20x^27+6x^28+2x^29+5x^30

The gray image is a code over GF(2) with n=168, k=16 and d=64.
This code was found by Heurico 1.16 in 8.55 seconds.