The generator matrix

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

generates a code of length 21 over Z4[X]/(X^3+2,2X) who´s minimum homogenous weight is 16.

Homogenous weight enumerator: w(x)=1x^0+25x^16+32x^19+384x^21+21x^22+32x^23+6x^24+10x^30+1x^38

The gray image is a code over GF(2) with n=168, k=9 and d=64.
This code was found by Heurico 1.16 in 3.81e-009 seconds.