The generator matrix

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

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+101x^16+1026x^17+2773x^18+7138x^19+13232x^20+16646x^21+13793x^22+7276x^23+2402x^24+902x^25+199x^26+34x^27+8x^28+2x^29+3x^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 8.56 seconds.