The generator matrix

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

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+20x^16+10x^17+25x^18+66x^19+85x^20+620x^21+84x^22+60x^23+19x^24+10x^25+15x^26+2x^27+3x^28+3x^30+1x^38

The gray image is a code over GF(2) with n=168, k=10 and d=64.
This code was found by Heurico 1.16 in 0.015 seconds.