The generator matrix

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

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+42x^16+490x^17+1523x^18+3318x^19+6570x^20+8800x^21+6766x^22+3278x^23+1413x^24+482x^25+63x^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 2.28 seconds.